Question

$\sin( \alpha ) = \cos( \beta ) \: then \: what \: is \: the \: value \: of \: \alpha + \beta$​

Answer 1

Answer:

$\alpha + \beta = 90$

Step-by-step explanation:

Given,

$sin\alpha = cos\beta$

To Find :-

Value of :-

$\alpha + \beta$

Solution :-

we know that :-

$cos\theta = sin(90 - \theta)$

$\implies cos\beta = sin(90 - \beta)$

Substituting the value :-

$sin\alpha = sin(90 - \beta)$

cancelling "sin" on both sides:-

$\alpha = 90 - \beta$

Transposing beta to left side :-

$\alpha + \beta = 90$