Question

prove that 1 + tan 2 A / 1 + cot2 A =tan2 A ​

Answer 1

Answer:

hence proved.....

I hope it will help you...!!!

Answer 2

$\LARGE{\bf{\underline{\underline{TO \ FIND:-}}}}$

• $\sf \dfrac{1+tan^2A}{1+cot^2A}=?$

$\LARGE{\bf{\underline{\underline{SOLUTION:-}}}}$

$\to \sf \dfrac{1+tan^2A}{1+cot^2A}$

▣ We know that 1+cot²A=cosec²A and 1+tan²A=sec²A. Thus, substitute.

$\to \sf \dfrac{sec^2A}{cosec^2A}$

▣ We know that $\sf cosecA=\dfrac{1}{sinA}$  and  $\sf secA=\dfrac{1}{cosA}$. Thus, substitute.

$\to \sf \dfrac{\dfrac{1}{cos^2A} }{\dfrac{1}{sin^2A} }$

$\to \sf \dfrac{sin^2A }{cos^2A }$

▣ Here, $\sf \dfrac{sin \theta }{cos \theta} = tan \theta$. So, we can simplify the above equation as:

$\to \sf{\red{tan^2A}}$

∴ (1+tan²A)÷(1+cot²A) is equal to tan²A

Funadamental trigonometric identities:

$\boxed{\substack{\displaystyle \sf sin^2 \theta+cos^2 \theta = 1 \\\\ \displaystyle \sf 1+cot^2 \theta=cosec^2 \theta \\\\ \displaystyle \sf 1+tan^2 \theta=sec^2 \theta}}$