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Question: If \(\cos 120^{o} = - \frac{1}{2}\)and \(\cos(180^{o} + 60^{o})\), then x =...

If cos⁡120o=−12\cos 120^{o} = - \frac{1}{2}and cos⁡(180o+60o)\cos(180^{o} + 60^{o}), then x =

A

=−cos⁡60o=−12= - \cos 60^{o} = - \frac{1}{2}

B

cos⁡240o=−12.\cos 240^{o} = - \frac{1}{2}.

C

θ=120o\theta = 120^{o}

D

240o240^{o}

Answer

=−cos⁡60o=−12= - \cos 60^{o} = - \frac{1}{2}

Explanation

Solution

We have, tan⁡(θ+φ)=1\tan(\theta + \varphi) = 1

Now check by options, put ⇒\Rightarrow

then θ+φ=π4\theta + \varphi = \frac{\pi}{4}

⇒ tan⁡(πcos⁡θ)=tan⁡(π2−πsin⁡θ)\tan(\pi\cos\theta) = \tan\left( \frac{\pi}{2} - \pi\sin\theta \right) ⇒ 30 = 30

Hence (1) is the correct answer.