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# 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)

(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

(i)

(ii)

(iii)

### Solution 6

Given that AB = BC = x

(i)

(ii)

(iii)

### 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)

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

(i)

(ii)

(iii)

(iv)

(V)

(vi)

(vii)

(viii)

(i)

(ii)

(iii)

(iv)

(v)

(i)

(ii)

(iii)

(i)

(ii)

(iii)

(i)

(ii)

(iii)

(i)

(ii)

(iii)

## Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise Test Yourself

(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

(i)

(ii)

(iii)

(iv)

(i)

(ii)

(iii)

(iv)

(i)

(ii)

(iii)

(iv)

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(xii)

(i)

(ii)

(iii)

(iv)

(i)

From

(ii)

(iii)

(iv)

### Solution 11

Adding (1) and (2)