Question

prove that tan 81° is equals to cot 9 °​

Answer 1

$\star\:\:\bf\large\underline\blue{Given\:To\:Prove:-}$

• $\tan(81 \degree) = \cot(9 \degree)$

$\star\:\:\bf\large\underline\blue{Solution:-}$

Before we start, we have to know the complete angle formulae.

• Two angles are said to be complementary angle if their sum is 90°

Now, we have to use this identity to solve this problem, i.e.,

$\tan(90 \degree - \theta) = \cot \theta$

Now, we can write $\tan(81\degree)$ as

$\tan(90 \degree - 9 \degree)$

$= \cot(9 \degree)$

Now, we can see that,

$\bf\underline\blue{LHS=RHS}$

$\star\:\:\bf\large\underline\blue{Hence\:Proved.}$

$\star\:\:\bf\large\underline\blue{Other\:Identity:-}$

• $\sin(90\degree-\theta)=\cos(\theta)$
• $\cosec(90\degree-\theta)=\sec(\theta)$

Answer 2

Answer:

answer for the given problem is given

Step-by-step explanation:

The sum of two angles is equal to 90° they are called complementary angles

the complementary angle of a is (90-a)