Question

if sin alpha=1\2 and cos beta=1\2 then alpha + beta =

Answer 1

Sin alpha = 1/2

Sin alpha = sin 30°

Alpha = 30°

Cos alpha = 1/2

Cos beta = cos 60°

Beta = 60°


Now, alpha + beta
= 30°+60°
= 90°

Answer 2

If sin alpha=1\2 and cos beta=1\2 then alpha + beta = 90

Solution:

In the question it is given that

$\sin \alpha=\frac{1}{2} \text { and } \cos \beta=\frac{1}{2}$

We have to find the value of $(\alpha+\beta)$

It is given that $\sin \alpha=\frac{1}{2}$

$\begin{array}{l}{\alpha=\sin ^{-1} \frac{1}{2}} \\\\ {\alpha=30^{\circ}}\end{array}$

It is given that $\cos \beta=\frac{1}{2}$

$\begin{array}{l}{\beta=\cos ^{-1} \frac{1}{2}} \\\\ {\beta=60^{\circ}} \\\\ {(\alpha+\beta)=30^{\circ}+60^{\circ}} \\\\ {(\alpha+\beta)=90^{\circ}}\end{array}$

Thus the value of $( \alpha + \beta)$ = 90°