the value of theta for which cos(10°+theta) = sin 30° is
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The value of θ = 50°
Given:
Cos(10°+θ) = sin 30°
To find:
The value of θ
Solution:
Given Cos(10°+θ) = sin 30°
As we know Sin 30° = 1/2
⇒ Cos(10°+θ) = 1/2
And we also know that Cos 60° = 1/2
⇒ Cos(10°+θ) = Cos 60°
⇒ 10° + θ = 60°
⇒ θ = 60° - 10° = 50°
⇒ The value of θ = 50°
We can check it by substituting θ = 50° in given expression
Cos(10°+θ) = Sin 30° ⇒ Cos(10°+50°) = Sin 30°
⇒ Cos 60° = Sin 30° = 1/2
Therefore, the value of θ = 50°
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