Question

if tan tita + cot tita = 2sin^2 tita + 2cos^2 tita then find tan^4 tita + cot^4 tita

Answer 1

Tan + cot = 2 sin^2 + 2cos^2

Tan + cot = 2 (sin^2 + cos^2)

Tan + cot = 2

on squaring both side

(tan + cot)^2 = 4

tan^2 + cot^2 + 2×tan×cot = 4

tan^2 + cot^2 = 4-2

tan^2 + cot^2 = 2

Again squaring both side

(tan^2 + cot^2)^2 = 4

tan^4 + cot^4 + 2×tan^2 × cot^2 = 4

tan^4 + cot^4 + 2 =4

tan^4 + cot^4 = 2

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