First slide

Trignometry

Question

if $θ_{1} + θ_{2} = \frac{π}{2} and θ_{1} = 2 θ_{2}$ ,then value of $\sin^{2} θ_{1} + \cos^{2} θ_{2}$ is :

Moderate

A

$\frac{1}{2}$
B

1
C

$\frac{3}{2}$
D

2

Solution

$θ_{1} + θ_{2} = \frac{π}{2} and θ_{1} = 2 θ_{2}$
$\Rightarrow θ_{1} = \frac{π}{3} and θ_{2} = \frac{π}{6}$
$So {Sin}^{2} θ_{1} + \cos^{2} θ_{2} = \frac{3}{4} + \frac{3}{4} = \frac{3}{2}$

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