Question

For the given statements select the correct option.

Assertion : In a right angled triangle ABC, if $cosA=\frac{1}{2}$ then, $sinB=\frac{1}{2}$.

Reason : $sin{30}^o=cos{60}^o$

• A. Both assertion and reason are true but reason is not the correct explanation of assertion.
• B. Assertion is false but reason is true
• C. Both assertion and reason are true and reason is the correct explanation of assertion.
• D. Assertion is true but reason is false.

Answer 1

The correct option is C

Both assertion and reason are true and reason is the correct explanation of assertion.

Let us consider a triangle ABC, right angled at C.

It is given that, $cosA=\frac{1}{2}$ then we can say that angle A = ${60}^o$.

We know that, sum of all the angles of any tringle is equal to ${180}^o$

Now, applying angle sum property in triangle ABC.
$\Rightarrow angleA+angleB+angleC={180}^o$

$\Rightarrow {60}^o+angleB+{90}^o={180}^o$

$\Rightarrow angleB={30}^o$

Hence, $sinB=\frac{1}{2}$

Therefore, Assertion is correct and reason is the correct explanation for the assertion.