Question

Simplify:
(1-sin^2 x)/(1+tan^2 x)

Answer 1

Given that 1 - sin²∅/1 + tan²∅

Now,

sin²∅ + cos²∅ = 1

→cos²∅ = 1 - sin²∅............[1]

Also,

sec²∅ - tan²∅ = 1

→sec²∅ = 1 + tan²∅............[2]

Thus,

(1 - sin²∅)/(1 + tan²∅)

•From [1] and [2],we get:

→cos²∅/sec²∅

→ cos⁴∅

Hence,(1 - sin²∅)/1 + tan²∅) = cos⁴∅

Answer 2

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