Question

cos ( α+ β )= 0 ,find sin ( α -β)

Answer 1

Answer:

1

Step-by-step explanation:

Given cos(alpha + beta) = 0

          cos(alpha + beta) = cos 90

                alpha + beta = 90

                alpha = 90 - beta  ------------- (1).

Now,

Given sin(alpha + beta)  ----------- (2)

Substitute (1) in (2), we get

sin(90 - beta + beta)

sin(90)

1.

Answer 2

SOLUTION:-

Given:

cos(alpha+beta)=0

$cos( \alpha + \beta ) = 0 \\ = > cos( \alpha + \beta ) = cos90 \degree \: \: \: \: \: \: \: [cos90 \degree = 0] \ \\ = > \alpha + \beta = 90 \degree \\ = > \alpha = 90 \degree - \beta ............(1) \\ \\ Now, \\ = > sin( \alpha - \beta ) = sin[(90 \degree - \beta ) - \beta ] \: \: \: \: \: \: \: \: \: \: [using \: (1)]\\ = > sin( \alpha - \beta ) = sin(90 \degree - 2 \beta ) \\ = > sin( \alpha - \beta ) = cos2 \beta \: \: \: \: \:[sin(90 \degree - \theta) = cos \theta]$

Hope it helps ☺️