Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

write all the trigonometric identities and prove that (1/ sec^2 theta - cos ^2 theta ( + )1/ cosec^2 theta - sin^2 theta) sin^2 theta. cos ^2 theta = 1 - sin^2 theta. cos^2 theta / 2+ sin^2 theta . cos^2 theta by using trigonometric identities
Asked by abhishekpareekv | 10 Oct, 2020, 02:04: PM
Expert Answer
To Prove
 
begin mathsize 14px style fraction numerator cos squared theta space sin squared theta over denominator s e c squared theta space minus space cos squared theta end fraction plus fraction numerator cos squared theta space sin squared theta over denominator cos e c squared theta space minus space sin squared theta end fraction space equals space fraction numerator 1 space minus space cos squared theta space sin squared theta over denominator 2 plus cos squared theta space sin squared theta end fraction end style  ..........................(1)
 
Let us use the relation secθ = 1/cosθ  and cosecθ = 1 / sinθ in LHS .  
 
LHS becomes
 
begin mathsize 14px style fraction numerator cos to the power of 4 theta space sin squared theta space over denominator 1 space minus space cos to the power of 4 theta end fraction plus space fraction numerator sin to the power of 4 theta space cos squared theta space over denominator 1 space minus space sin to the power of 4 theta end fraction equals space fraction numerator cos to the power of 4 theta space space over denominator 1 space plus space cos squared theta end fraction plus space fraction numerator sin to the power of 4 theta space space over denominator 1 space plus space sin squared theta end fraction space equals space fraction numerator cos to the power of 4 theta space plus space cos to the power of 4 theta space sin squared theta space plus sin to the power of 4 theta cos squared theta space plus space space sin to the power of 4 theta over denominator left parenthesis space 1 space plus space cos squared theta space right parenthesis space left parenthesis space 1 space plus space sin squared theta space right parenthesis end fraction end style ..................(2)
 
Let us consider the following relations
 
Error converting from MathML to accessible text. .................(3)
begin mathsize 14px style cos to the power of 4 theta space sin to the power of 4 theta space space plus space sin to the power of 4 theta space cos to the power of 4 theta space equals space cos squared theta space sin squared theta space left parenthesis space cos squared theta space plus space sin squared theta right parenthesis space equals space cos squared theta space sin squared theta end style .................(4)
begin mathsize 14px style left parenthesis space 1 space plus space cos squared theta space right parenthesis space left parenthesis space 1 space plus space sin squared theta space right parenthesis space equals space left parenthesis space 1 space plus space cos squared theta space plus space sin squared theta space plus space cos squared theta space sin squared theta space right parenthesis space equals space left parenthesis space 2 space plus space cos squared theta space sin squared theta space right parenthesis end style ............. (5)
By using relations (3), (4) and (5) in the right most part of relation-(2) , we rewrite relation (2) as
 
begin mathsize 14px style fraction numerator cos to the power of 4 theta space sin squared theta space over denominator 1 space minus space cos to the power of 4 theta end fraction plus space fraction numerator sin to the power of 4 theta space cos squared theta space over denominator 1 space minus space sin to the power of 4 theta end fraction equals space space fraction numerator 1 space minus space cos squared theta space sin squared theta over denominator 2 space plus space space cos squared theta space sin squared theta end fraction end style
Answered by Thiyagarajan K | 15 Oct, 2020, 12:58: PM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test Subjective Questions Webinar Subjective Questions Pre Board Assessment
Answered Unanswered My Questions My Answers
CBSE 10 - Maths
cot2 30-2cos2 60-3/4sec2 45-4sec2 30
Asked by Akhandp457 | 29 May, 2023, 09:06: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
find the zeroes of the quadratic polynomial and verify the relationship between the zeroes and the coffiecient 4u+8u
Asked by dimpaldihingia2 | 24 May, 2023, 06:10: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
if sin theta = root3/2, find the value of all t- ratios
Asked by akhilthainuan | 22 May, 2023, 02:11: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
If α and β are tge zeros of the polynomial x^2 - 6x + k and 3α + 2β=20 , then the value of k is
Asked by ruchipandey20071978 | 21 May, 2023, 10:00: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
If one of the zeros of the quadratic polynomial (k - 1)x^2 + kx + 1 is -3, then the value of k
Asked by ruchipandey20071978 | 21 May, 2023, 09:57: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
If the sum of the zeors of the polynomial f (x)=2x^3 - 3kx^2 +4x - 5 is 6 , then the value of k is
Asked by ruchipandey20071978 | 21 May, 2023, 05:32: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
If two zeros of x^3 + x^2 - 5x - 5 are √5 and - √5, then its third zero is
Asked by ruchipandey20071978 | 21 May, 2023, 05:29: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
The value of k for which the system of equestions kx-y=2 and 6x-2y=3 has a uniqe solution is..
Asked by ruchipandey20071978 | 11 May, 2023, 06:55: AM
ANSWERED BY EXPERT
CBSE 10 - Maths
a regular polygon has 20 sides. how many triangles can be drawn by using the vertices but not using the sides?
Asked by gavhanenisha0310 | 09 May, 2023, 04:10: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial. 1) The graph of the parabola opens upwards, if _______. (a) a = 0 (b) a < 0 (c) a > 0 (d) a ≥ 0 2) Observe the following graph and answer. In the above graph how many zeroes are there for the polynomial ? (a) 0 (b) 1 (c) 2 (d) 3 3) The three zeroes in the above shown graph are (a) 2, 3, -1 (b) -2, 3, 1 (c) -3, -1, 2 (d) -2, -3, -1 4) What will be the expression of the polynomial (a) x³ + 2x² - 5x - 6 (b) x³ + 2x² - 5x + 6 (c) x³ + 2x² + 5x - 6 (d) x³ + 2x² + 5x + 6
Asked by susrisangita792 | 08 May, 2023, 06:54: PM
ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt