Solveeit Logo
Login

Question

Question: If \(\cos\theta = \cos\left( \frac{\pi}{4} \right)\)then the most general value of \(\Rightarrow\) i...

If cos⁡θ=cos⁡(π4)\cos\theta = \cos\left( \frac{\pi}{4} \right)then the most general value of ⇒\Rightarrow is.

A

θ=2nπ±π4\theta = 2n\pi \pm \frac{\pi}{4}

B

θ=π4\theta = \frac{\pi}{4}

C

2nπ±π42n\pi \pm \frac{\pi}{4}

D

tan⁡θ=cot⁡α⇒tan⁡θ=tan⁡(π2−α)\tan\theta = \cot\alpha \Rightarrow \tan\theta = \tan\left( \frac{\pi}{2} - \alpha \right)

Answer

tan⁡θ=cot⁡α⇒tan⁡θ=tan⁡(π2−α)\tan\theta = \cot\alpha \Rightarrow \tan\theta = \tan\left( \frac{\pi}{2} - \alpha \right)

Explanation

Solution

⇒\Rightarrow{dividing by

sin⁡θ−cos⁡θ=−2\sin\theta - \cos\theta = - \sqrt{2}

⇒\Rightarrow 12sin⁡θ−12cos⁡θ=−1\frac{1}{\sqrt{2}}\sin\theta - \frac{1}{\sqrt{2}}\cos\theta = - 1

⇒\Rightarrow 12cos⁡θ−12sin⁡θ=1⇒cos⁡(θ+π4)=cos⁡(0)\frac{1}{\sqrt{2}}\cos\theta - \frac{1}{\sqrt{2}}\sin\theta = 1 \Rightarrow \cos\left( \theta + \frac{\pi}{4} \right) = \cos(0).