Question

If (a+b)=90° and a=2b find cos²a+ sin²b

Answer 1

a+b=90°...(1)

a=2b...(2)

using eq2 in eq1

we get

2b+b=90

3b=90

b=30°

use value of b in eq2

we get

a=60°

now,

cos^2a+sin^2b

cos^260°+sin^230°

1/2^2+1/2^2

1/4+1/4

2/4

1/2 is the answer

Answer 2

Answer:

Given,

a+b= 90°

a= 2b

2b+b= 90°

3b= 90°

b= 30°

a=2b

a= 2(30°)

a=60°

Explanation:

to find the value of

${ \cos }^{2} a + { \sin }^{2} b \\ { \cos }^{2} 60 + { \sin }^{2} 30$

value of cos 60° = 1/2

value of sin 30° = 1/2

putting the values in the equation,

$({ \frac{1}{2} )}^{2} + ({ \frac{1}{2})}^{2} = \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$

answer is 1/2