Question

Solve d number right answer will be marked brainliest

Answer 1

Answer:

Step-by-step explanation:

We have

$\tt{\dfrac{sec(4\theta)-1}{sec(2\theta)-1}}$

$\sf{=\dfrac{\dfrac{1}{cos(4\theta)}-1}{\dfrac{1}{cos(2\theta)}-1}}$

$\sf{=\dfrac{\big(1-cos(4\theta)\big)\cdot\,cos(2\theta)}{\big(1-cos(2\theta)\big)\cdot\,cos(4\theta)}}$

$\sf{=\dfrac{2\,sin^2(2\theta)\cdot\,cos(2\theta)}{2\,sin^2(\theta)\cdot\,cos(4\theta)}}$

$\sf{=\dfrac{sin(2\theta)\cdot2\,sin(2\theta)\,cos(2\theta)}{2\,sin^2(\theta)\cdot\,cos(4\theta)}}$

$\sf{=\dfrac{sin(2\theta)\cdot\,sin(4\theta)}{2\,sin^2(\theta)\cdot\,cos(4\theta)}}$

$\sf{=\dfrac{2\,sin(\theta)\,cos(\theta)\cdot\,sin(4\theta)}{2\,sin^2(\theta)\cdot\,cos(4\theta)}}$

$\sf{=\dfrac{cos(\theta)\cdot\,sin(4\theta)}{sin(\theta)\cdot\,cos(4\theta)}}$

$\sf{=\dfrac{cos(\theta)}{sin(\theta)}\cdot\dfrac{sin(4\theta)}{cos(4\theta)}}$

$\sf{=cot(\theta)\cdot\,tan(4\theta)}$

$\sf{=tan(4\theta)\,cot(\theta)}$