Class 9 SELINA Solutions Maths Chapter 23: Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise Ex. 23(A)
Solution 1(a)
Correct option: (i) sin 60o
Solution 1(b)
Correct option: (ii) 20o
Solution 1(c)
Correct option: (iii) 45o
Solution 1(d)
Correct option: (iii) 3
Solution 1(e)
Correct option: (i) 
Solution 2
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Solution 3
(i) 
(ii) 
(iii) 3 sin2 30o + 2 tan2 60o - 5 cos2 45o
Solution 4
(i)LHS=sin 60o cos 30o + cos 60o. sin 30o
=
(ii)LHS=cos 30o. cos 60o - sin 30o. sin 60o
=
=RHS
(iii)LHS= cosec2 45o - cot2 45o
=
=RHS
(iv)LHS= cos2 30o - sin2 30o
=
=RHS
(v)LHS= 
=
=RHS
(vi)LHS= 
=
=RHS
Solution 5
(i)
(ii)
(iii)
Solution 6
Given that AB = BC = x
(i) 
(ii) 
(iii) 
Solution 7
Solution 8
(i)
The angle, x is acute and hence we have, 0 < x
(ii)
(iii)
(iv)
Solution 9
(i)
if x and y are acute angles,
is false.
(ii)
Sec
. Cot = cosec is true
(iii)
Solution 10
(i)
For acute angles, remember what sine means: opposite over hypotenuse. If we increase the angle, then the opposite side gets larger. That means "opposite/hypotenuse" gets larger or increases.
(ii)
For acute angles, remember what cosine means: base over hypotenuse. If we increase the angle, then the hypotenuse side gets larger. That means "base/hypotenuse" gets smaller or decreases.
(iii)
For acute angles, remember what tangent means: opposite over base. If we decrease the angle, then the opposite side gets smaller. That means "opposite /base" gets decreases.
Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise Ex. 23(B)
Solution 1(a)
Correct option: (i) cot A
Solution 1(b)
Correct option: (i) cot A
Solution 1(c)
Correct option: (iii) sin 3A
Solution 1(d)
Correct option: (iv) cos 60o
Solution 1(e)
Correct option: (i) 1
Solution 2
Given A = 60o and B = 30o
(i)
(ii)
(iii)
(iv)
Solution 3
Given A=
(i)
(ii)
(iii)
(iv)
Solution 4
Given that A = B = 45o
(i)
(ii)
Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise Ex. 23(C)
Solution 1(a)
Correct option: (i) 30o
Solution 1(b)
Correct option: (i) 90o or 0o
Solution 1(c)
Correct option: (ii) 45o
Solution 1(d)
Correct option: (iii) 10o
Solution 1(e)
Correct option: (iv) 30o
Solution 2
(i)
(ii)
(iii)
(iv)
(V)
(vi)
(vii)
(viii)
Solution 3
(i)
(ii)
(iii)
(iv)
(v)
Solution 4
(i)
(ii)
(iii)
Solution 5
(i)
(ii)
(iii)
Solution 6
Solution 7
(i)
(ii)
(iii)
Solution 8
(i)
(ii)
(iii)
Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise Test Yourself
Solution 1
(i)
(ii)
Solution 2
(i) Given that A=
(ii) Given that B=
Solution 3
Given that A = 30o
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
Solution 4
(i)
Given that x = 30o
(ii)
Given that B = 90o
Solution 5
(i)
(ii)
(iii)
(iv)
Solution 6
(i)
(ii)
(iii)
(iv)
Solution 7
(i)
(ii)
(iii)
(iv)
Solution 8
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
(xi)
(xii)
Solution 9
(i)
(ii)
(iii)
(iv)
Solution 10
(i)
From
(ii)
(iii)
(iv)
Solution 11
Adding (1) and (2)
