Question

if tan ∅ +cot∅=5 then find the value of $tan^{2}$∅+$cot^{2}$∅

Answer 1

Answer:

The required numeric value of tan^2 A + cot^2 A is 23.

Step-by-step explanation:

It is given that the value of tanA + cotA is 5.

= > tanA + cotA = 5

Square on both sides : -

= > ( tanA + cotA )^2 = 5^2

From the properties of expansions :

( a + b )^2 = a^2 + 2ab + b^2

= > tan^2 A + cot^2 A + 2 tanA cotA = 25

= > tan^2 A +  cot^2 A + 2( tanA x 1 / tanA ) = 25

= > tan^2 A + cot^2 A + 2 ( 1 ) = 25

= > tan^2 A + cot^2 A + 2 = 25

= > tan^2 A + cot^2 A = 25 - 2

= > tan^2 A + cot^2 A = 23

Hence,

The required numeric value of tan^2 A + cot^2 A is 23.

Answer 2

The answer is 23.
Steps in the attachment.