Question

If sec theta + tan theta equal to 2 then prove that cosec theta + cot theta equal to 3

Answer 1

Hey mate!!!

Here's the answer!!!

Hope this helps you.

Also, here θ = 30(n + 12) for any integer n.

Thank you...

$\mathsc{\#adithyasajeevan}$

Answer 2

Answer:

Given that $sec\,\theta+tan\,\theta=2$

To prove: $cosec\,\theta+cot\,\theta=3$

we know $sex^2\,\theta-tan^2\,\theta=1$

$(sec\,\theta+tan\,\theta)(sec\,\theta-tan\,\theta)=1$

$2(sec\,\theta-tan\,\theta)=1$

$sec\,\theta-tan\,\theta=\frac{1}{2}$

now consider,

$(sec\,\theta+tan\,\theta)+(sec\,\theta-tan\,\theta)=2+\frac{1}{2}$

$sec\,\theta=\frac{4+1}{2}$

$2sec\,\theta=\frac{5}{2}$

$sec\,\theta=\frac{5}{4}$

$\frac{1}{cos\,\theta}=\frac{5}{4}$

$cos\,\theta=\frac{4}{5}$

Consider,

$sec\,\theta+tan\,\theta=2$

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

$\frac{5}{4}+\frac{5sin\,\theta}{4}=2$

$5+5sin\,\theta=8$

$1+sin\,\theta=\frac{8}{5}$

$sin\,\theta=\frac{8-5}{5}$

$sin\,\theta=\frac{3}{5}$

Now,

$cosec\,\theta+cot\,\theta$

$\implies\frac{1}{sin\,\theta}+\frac{cos\,\theta}{sin\,\theta}$

$\implies\frac{5}{3}+\frac{\frac{4}{5}}{\frac{3}{5}}$

$\implies\frac{5}{3}+\frac{4}{3}$

$\implies\frac{9}{3}$

$\implies3$

Hence Proved