Question

1+cot^2÷1+tan^2 is equal to
​

Answer 1

Answer:

cot²a

Step-by-step explanation:

1+cot²a=cosec²a

1+tan²a=sec²a

cosec²a/sec²a=cot²a

Answer 2

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

• $\sf \dfrac{1+cot^2A}{1+tan^2A}$

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

• $\sf \dfrac{1+cot^2A}{1+tan^2A}=?$

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

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

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

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

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

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

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

▣ Here, $\sf \dfrac{cos \theta }{sin \theta} = cot \theta$. So, we get:

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

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

Trigonometric identities:

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