Simplify the expression: (tanx/csc^2x) +(tanx/sec^2x)

Answer 1

Greetings! Lets solve this shall we ?

So, we must simplify the given expression as much as we can in this scenario! So, we have

(tanx / csc²x) + (tanx / sec²x) ...........Let switch everything in terms of sine and cosine such that

(sinx/cosx) / (1/sin²x) + (sinx/cosx) / (1/cos²x).........Then we apply the Keep-Flip-Change method such that

(sinx/cosx)*(sin²x/1) + (sinx/cosx)*(cos²x/1)........Now we simplify to get

(sin³x / cosx) + (sinxcos²x / cosx)............Now that we have a common denominator, we get

(sin³x + sinxcos²x) / cosx.........Then we factor out a sinx such that

sinx(sin²x + cos²x) / cosx.........sin²x + cos²x = 1 from the trig identities right ? So we use that to obtain

sinx / cosx = tanx

I hope this helped!