Question

if, tan(πcostheta)= cot(πsintheta)
then prove that,
sin(theta+π/4) = 1/2√2
​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

tan($\pi$cos$\theta$) = cot($\pi$sin$\theta$)

$\frac{sin(\pi cos\theta)}{cos(\pi cos\theta)}$ = $\frac{cos(\pi sin\theta)}{sin(\pi sin\theta)}$

cos($\pi sin\theta$)*cos($\pi cos\theta$) - sin($\pi$sin$\theta$)*sin($\pi$cos$\theta$) = 0

cos($\pi sin\theta + \pi cos\theta$) = 0 = cos($\pi/2$) (Considering only principal solution)

$\pi$(sin$\theta$ + cos$\theta$) = $\frac{\pi}{2}$

sin$\theta$ + cos = $\frac{1}{2}$

$\frac{1}{\sqrt{2} }$ sin$\theta$ + $\frac{1}{\sqrt{2} }$ cos$\theta$ = $\frac{1}{2\sqrt{2} }$

cos($\pi /4$)sin$\theta$ + sin($\frac{\pi}{4}$)cos$\theta$ = $\frac{1}{2\sqrt{2} }$

Hence, sin($\theta$+$\frac{\pi}{4}$) = $\frac{1}{2\sqrt{2} }$