Question

sin2a/cos2a + cos2a/sin2a =sec2a -cosec2a -2

Answer 1

(1-cos²α) (sec²α-1)

----------------------------- = tan^4α

cos²α

3 answers · Mathematics

Best Answer

Proof:

(1-cos²α) (sec²α-1)

----------------------------- = LHS

(cos²α)

In the numerator, the following substitutions take place. sin²α + cos²α = 1. Hence, 1 - cos²α = sin²α. Similarly, 1 + tan²α = sec²α. Hence, sec²α - 1 = tan²α

(sin²α) (tan²α)

= --------------------

(cos²α)

(sinα)/(cosα) = tanα. Hence, by squaring we get (sin²α)/(cos²α) = tan²α. Using this in the given case, we have,

= (tan²α) (tan²α)

= (tan^4α)

= RHS