Question

if sin [20 + theta] = cos 30 degree, then find the value of theta.

Answer 1

sin ( 20+ theta) = cos 30 degree
=> sin ( 20+theta) = cos (90- 30 degree)
=> sin (20+theta)= sin ( 90-30)
=> 20+theta = 90-30
=> theta = 60-20
=> theta = 40
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Answer 2

The value of $\theta$ is $40^{\circ}$.

Step-by-step explanation:

Given,

$sin ( 20^{\circ}+ \theta) = cos 30^{\circ}$

We have to find $\theta$.

Now according to the problem, we have

⇒ $sin ( 20^{\circ}+ \theta) = cos 30^{\circ}$

⇒ $sin ( 20^{\circ}+\theta) = cos (90^{\circ}- 60^{\circ})$

⇒ $sin ( 20^{\circ}+\theta) = sin (60^{\circ})$                    $[cos (90^{\circ} - \theta) = sin\theta]$

⇒ $20^{\circ}+\theta = 60^{\circ}$

⇒ $\theta = 60^{\circ} - 20^{\circ}$

⇒ $\theta = 40^{\circ}$

Hence, the value of $\theta$ is $40^{\circ}$.

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