Can someone help me with these 3 trig identities?

Question

i have 3 left out of my 80 problems & these ones i just can't seem to figure out..


1. 1/2 ÷ 1 - sinA + 1/2 ÷ 1 + sinA = 1+tan²a

2. 4tan^4 Θ + tan²Θ -3 = sec²Θ(4tan²Θ-3)


3. sinx(cotx + tanx) = secx

Answer 1

let me help you with the third one:

sinx ( cosx/sinx + sinx/cosx)=sec x

Equate the denominators

sinx ( (cos^x+sin^x) / (sinxcosx) )= secx

sinx ( 1/(sinx cosx))=sec x

Cancel sinx

1/cosx = sec x

sec x = secx

Yes, it is true
LHS=RHS

Hint : tan x= sinx/cosx

cot x=cosx/sinx

sin^x + cos^x =1

Answer 2

Ask in the Mathematics section under Science and Mathematics.