Trigonometric identities

Question

"Verify" cos²(x) (1+tan²(x))=1

Answer 1

cos²(x)(1 + tan²(x)) = 1

1 + tan²(x) = sec²(x)

substituting that we get,

cos²(x) sec²(x) = 1 ----------- eq(1)

sec²(x) = 1/cos²(x)

substituting that in the L.H.S of eq(1) we get,

cos²(x) . 1/cos²(x) = 1

LHS = RHS

Answer 2

To verify this identity, we begin by replacing the expression "1 + tan² x with sec² x ( according to one of the Pythagorean identities). We then rewrite sec² x as 1/cos² x according to the reciprocal identity for cos x. Substituting this into the original equation, we have (cos²x) ( 1/cos² x) = 1. Multiplying reciprocals always yields a product of 1, thus proving the identity.

Answer 3

Write tan(x) = sin(x)/cos(x) and simplify...