# 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

(i)

(ii)

(iii)

(iv)

(v)

(vi)

### Solution 2

(i)

(ii)

(iii) 3 sin^{2} 30^{o} + 2 tan^{2} 60^{o} - 5 cos^{2} 45^{o}

### Solution 3

(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 4

(i)

(ii)

(iii)

### Solution 5

Given that AB = BC = x

(i)

(ii)

(iii)

### Solution 6

### Solution 7

(i)

The angle, x is acute and hence we have, 0 < x

(ii)

(iii)

(iv)

### Solution 8

(i)

if x and y are acute angles,

is false.

(ii)

Sec. Cot = cosec is true

(iii)

### Solution 9

(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.

### Solution 10

(i)

(ii)

### Solution 11

(i) Given that A=

(ii) Given that B=

## Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise Ex. 23(B)

### Solution 1

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

(i)

(ii)

(iii)

(iv)

### Solution 2

Given A=

(i)

(ii)

(iii)

(iv)

### Solution 3

Given that A = B = 45^{o}

(i)

(ii)

### Solution 4

Given that A = 30^{o}

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

## Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise Ex. 23(C)

### Solution 1

(i)

(ii)

(iii)

(iv)

(V)

(vi)

(vii)

(viii)

### Solution 2

(i)

(ii)

(iii)

(iv)

(v)

### Solution 3

(i)

(ii)

(iii)

### Solution 4

(i)

(ii)

(iii)

### Solution 5

### Solution 6

(i)

(ii)

(iii)

### Solution 7

(i)

(ii)

(iii)

### Solution 8

(i)

Given that x = 30^{o}

(ii)

Given that B = 90^{o}

^{}

### Solution 9

(i)

(ii)

(iii)

(iv)

### Solution 10

(i)

(ii)

(iii)

(iv)

### Solution 11

(i)

(ii)

(iii)

(iv)

### Solution 12

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(xii)

### Solution 13

(i)

(ii)

(iii)

(iv)

### Solution 14

(i)

From

(ii)

(iii)

(iv)

### Solution 15

Adding (1) and (2)