Ask a Doubt
Request a call back

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

CBSE Class 12-science Answered

Can anyone pls explain me how to solve the following Q stepwise.
 
If x=2 log subscript e left parenthesis tan left parenthesis theta divided by 2 right parenthesis right parenthesis and y=sin left parenthesis theta right parenthesis find d squared y divided by d x squared at theta=straight pi divided by 2.
 
Asked by Bhuvan K Iyer | 17 Feb, 2015, 06:27: PM
answered-by-expert Expert Answer
G i v e n space x equals 2 log subscript e open parentheses tan open parentheses theta over 2 close parentheses close parentheses space a n d space y equals sin theta W e space n e e d space t o space f i n d space fraction numerator d squared y over denominator d x squared end fraction. fraction numerator d x over denominator d theta end fraction equals fraction numerator 2 over denominator tan open parentheses theta over 2 close parentheses end fraction cross times s e c squared open parentheses theta over 2 close parentheses cross times 1 half space space space space space space space equals fraction numerator 1 over denominator sin open parentheses theta over 2 close parentheses cos open parentheses theta over 2 close parentheses end fraction space space space space space space space equals fraction numerator 1 over denominator begin display style fraction numerator sin theta over denominator 2 end fraction end style end fraction rightwards double arrow fraction numerator d x over denominator d theta end fraction equals fraction numerator 2 over denominator begin display style sin theta end style end fraction fraction numerator d y over denominator d theta end fraction equals cos theta fraction numerator d y over denominator d x end fraction equals fraction numerator fraction numerator d y over denominator d theta end fraction over denominator fraction numerator d x over denominator d theta end fraction end fraction space space space space space space equals fraction numerator cos theta over denominator fraction numerator 2 over denominator begin display style sin theta end style end fraction end fraction space space space space space space equals fraction numerator sin theta cos theta over denominator 2 end fraction space space space space space space equals fraction numerator sin 2 theta over denominator 2 end fraction fraction numerator d squared y over denominator d x squared end fraction equals fraction numerator d over denominator d x end fraction open parentheses fraction numerator d y over denominator d x end fraction close parentheses space space space space space space space space space equals fraction numerator d over denominator d theta end fraction open parentheses fraction numerator sin 2 theta over denominator 2 end fraction close parentheses cross times fraction numerator d theta over denominator d x end fraction space space space space space space space space space equals fraction numerator cos 2 theta over denominator 4 end fraction cross times fraction numerator sin theta over denominator 2 end fraction open square brackets fraction numerator d squared y over denominator d x squared end fraction close square brackets subscript theta equals straight pi over 2 end subscript equals fraction numerator cos 2 cross times straight pi over 2 over denominator 4 end fraction cross times fraction numerator sin straight pi over 2 over denominator 2 end fraction space space space space space space space space space space space space space space space space space space space space equals cosπ over 4 cross times fraction numerator sin straight pi over 2 over denominator 2 end fraction space space space space space space space space space space space space space space space space space space space space equals fraction numerator negative 1 over denominator 4 end fraction cross times 1 half space space space space space space space space space space space space space space space space space space space space equals fraction numerator negative 1 over denominator 8 end fraction
Answered by Vimala Ramamurthy | 18 Feb, 2015, 10:26: AM

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 12-science - Maths
How to solve two variables limits?
question image
Asked by fehasaf670 | 27 Jan, 2024, 01:39: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Differentiation
question image
Asked by tanyavishwakarma427 | 24 Nov, 2023, 11:56: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Solve please 
question image
Asked by sonkarmukesh007 | 13 Aug, 2023, 08:32: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
find dy/dx where y= (1+x) (1+2x) (1+3x)
question image
Asked by unqio66 | 15 May, 2023, 11:48: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Find the derivative of log|-x|?
Asked by sdmbotch1123 | 21 Dec, 2022, 04:38: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
If e^x +e^y  =e^x+y Then prove         dy/dx  + e^y-x =0
Asked by iasaspirant20s | 09 Oct, 2022, 02:31: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
X√1+y+y√1+x=0 then dy/dx=?
question image
Asked by Raunaksingh4742 | 25 Aug, 2022, 12:31: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
differentiation of Incosx
Asked by pinkidevnict | 08 Jun, 2022, 07:51: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
integration
Asked by suvajyotichaudhury998 | 04 Jun, 2022, 07:54: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
change of base formula
Asked by lewisraina069 | 03 Jun, 2022, 06:56: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×