Question

if cos(90-A)=0,then Sin (A+B)=______
a. 0, b. 2,c.3,d.none of the above​

Answer 1

Answer:

option d (none)

Step-by-step explanation:

Given,

cos(90° - A) = 0

To Find :-

Value of 'sin(A + B)'.

How To Do :-

As they given the value of 'cos(90° - A)' we need to expand it through the formula cos(C - D) and we need to find the value of 'A'. After obtaining the value of 'A' by using that we need to expand sin(A + B) and we need to find that value.

Formula Required :-

cos(C - D) = cosC.cosD + sinC.sinD

sin(C + D) = sinC.cosD + cosC.sinD

Solution :-

cos(90 - A) = 0

Expanding L.H.S by using cos(C - D) formula :-

cos90°.cosA + sin90°.sinA = 0

0.cosA + 1.sinA = 0

0 + sinA = 0

sinA = 0

sinA = sin0°

Cancelling 'sin' on both sides :-

A = 0°

Expanding 'sin(A + B)' using the formula 'sin(C + D)' :-

sin(A + B) = sinA.cosB + cosA.sinB

= sin0°.cosB + cos0°.sinB

= 0.cosB + 1.sinB

= 0 + sinB

= sinB

sin(A + B) = sinB

As 'sinB' is not there in options we need to choose it as "optiond"(none).

option 'd'