Question

if cos (90-A) =0. Then sin (A+B)= A) 0 B) 2 C) 3 D) none of these​

Answer 1

Answer: sin B...D) none of these

Step-by-step explanation:

Given :- cos(90 - A) = 0

To Find :- sin(A + B) = ?

we know that,

cos(90 - x) = sin x .

sin(x + y) = sin x * cos y + cos x * sin y

so,

→ cos(90 - A) = 0

→ sin A = 0 ---- Eqn.(1)

then,

→ sin(A + B)

→ sin A * cos B + cos A * sin B

putting value of Eqn.(1)

→ 0 * cos B + cos A * sin B

→ cos A * sin B ------ Eqn.(2)

now, since,

→ sin A = 0

→ sin A = sin 0°

→ A = 0°

therefore,

→ cos A * sin B

→ cos 0° * sin B

→ 1 * sin B

→ sin B

cos(90 - A ) = 0

sin A = 0

A = 0

 

sin(A + B)= sin A * cos B + cos A * sin B

= 0 * cos B + cos A * sin B

= cos A * sin B

= cos 0° * sin B

= 1 * sin B

= sin B

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