Question

:) Prove that tan x + cotx = secx .cosecx​

Answer 1

Answer:

convert tan and cot in sin and cos form

Taking LHS

tan x + cot x

sin x/cos x + cos x / sin x

taking LCM

sin^2x +cos^2 x / sinx cos x

here is identity

sin ^2x+cos^2x =1

1/ sin x cos x

1/sin x *1/cos x

here is identity 1/sin x = cosec x & 1/ cos x = sec x

cosec x sec x = RHS

Answer 2

Answer:

tanx + cotx = secx.cosecx

tanx = sinx/cosx

cotx = cosx/sinx

Putting the values

sinx/cosx + cosx/sinx

sin^2x + cos^2x / cosx.sinx

Since sin^2x + cos^2x = 1

1/cosx.sinx

secx.cosecx

Proved