# 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 60^{o}

### Solution 1(b)

Correct option: (ii)
20^{o}

### Solution 1(c)

Correct option: (iii)
45^{o}

### 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 sin^{2} 30^{o} + 2 tan^{2} 60^{o} - 5 cos^{2} 45^{o}

### Solution 4

(i)LHS=sin 60^{o} cos 30^{o} + cos 60^{o}. sin 30^{o}

=

(ii)LHS=cos 30^{o}. cos 60^{o} - sin 30^{o}. sin 60^{o}

==RHS

(iii)LHS= cosec^{2} 45^{o} - cot^{2} 45^{o}

==RHS

(iv)LHS= cos^{2} 30^{o} - sin^{2} 30^{o}

==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 60^{o}

### Solution 1(e)

Correct option: (i) 1^{}

### Solution 2

Given A = 60^{o} and B = 30^{o}

(i)

(ii)

(iii)

(iv)

### Solution 3

Given A=

(i)

(ii)

(iii)

(iv)

### Solution 4

Given that A = B = 45^{o}

(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) 30^{o}

### Solution 1(b)

Correct option: (i) 90^{o} or 0^{o}

### Solution 1(c)

Correct option:
(ii) 45^{o}

### Solution 1(d)

Correct option:
(iii) 10^{o}

### Solution 1(e)

Correct option:
(iv) 30^{o}

### 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 = 30^{o}

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

### Solution 4

(i)

Given that x = 30^{o}

(ii)

Given that B = 90^{o}

^{}

### 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)