If cos = 0, then value of cos is equal to Class 10 Maths Introduction to Trigonometry questions with solutions

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Solution

Q.
If cos $(α + β)$ = 0, then value of cos $(\frac{α + β}{2})$ is equal to:

1 $\frac{1}{\sqrt{2}}$

2 $\frac{1}{2}$

3 $0$

4 $\sqrt{2}$

Ans.
(1)

$\cos (α + β) = 0 = \cos 90 ° \Rightarrow (α + β) = 90 ° \Rightarrow \frac{α + β}{2} = 45 °$

$\Rightarrow \cos (\frac{α + β}{2}) = \cos 45 ° = \frac{1}{\sqrt{2}}$

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