Question

if Tan A=1/3 prove that cosec^2 A=1 + Cot^2 A​

Answer 1

Answer:

$\sf \: tan \: A=\frac{1}{3}$

Then cot A=3

We know that,,.

$\sf \boxed{ \red{ \sf sec {}^{2} a = 1 + tan {}^{2} a}}$

$1 + \bigg( \huge{\frac{1}{3}\bigg)} {}^{2}$

$1 \frac{1}{9} = \frac{10}{9}$

$\sf \: sec \: A \: = \frac{ \sqrt{10} }{3}$

$\sf \: then \: \pink{ \boxed{\sf \: sec \: A \: = \frac{3}{ \sqrt{10} } }}$

We know that.

$\sf \: cos {}^{2} a + sin {}^{2} a = 1$

$\sf \: sin {}^{2} a = 1 - cos {}^{2} a = 1$

$1 \frac{9}{10} = \frac{1}{10}$

$\sf \: sin \: a = \frac{1}{ \sqrt{10} }$

then cosec A =√10

LHS=COSEC^2A

=(√10)^2=10

RHS=1+cot^2A

T(3)^2=A+1

=10. ( From (1) and (2). )

LHS= RHS.

Hence, vertified