proving trig identities?

Question

prove the identity sin^20/1-cos0=sec 0+1/sec 0

Answer 1

To prove:-
sin ² θ / (1 - cos θ ) = (secθ + 1) / sec θ

LHS
( 1 - cos ² θ ) / (1 - cos θ )
( 1 - cos θ )(1 + cos θ ) / ( 1 - cos θ )
1 + cos θ

RHS
cos θ (1 / cos θ + 1)
1 + cos θ

LHS = RHS

Tip
To avoid chaos and confusion, use brackets in 2008!

Happy New Year

Answer 2

I am guessing that those 0 you have there are actually the Greek letter theta, and you left out some CRITICAL parentheses

lets just use x instead
sin^2 x/(1-cosx)=(sec x +1)/sec x

ok lets leave the right side alone and work with the left
1-cos^2 x/(1-cosx)= sub sin^2 x = 1-cos^2 x
(1+cos x) (1-cosx)/1-cos x= factor the numerator
1+cos x= cancel 1-cos
cos(1/cos+1)= factor out cos
(1/sec x)(sec x+1) sub sec for 1/cos
(secx+1)/sec x rearrange

Answer 3

sin^2 0 = 1 - cos^2 0; factor this and cancel out the bottom

Then replace the resulting cos 0 with 1/sec 0 and simplify

Answer 4

in this situation, i've got self belief you are going to be able to desire to apply the Pythagorean, Reciprocal, and Quotient Identities...as far as a textbook is in contact. very nearly, right here - take the two area of the id at a time: Sin^2(x) Sec^2(x) may be simplified to Tan^2 (x) as a results of fact secant is one million/cosine, for this reason you get Sin^2(x) / Cos^2(x). so that's now Tan^2(x) = sec^2(x) -one million. in accordance to the Pythag id, one million+tan^2(x) = Sec^2(x). it is definitely changed by utilizing subtracting 'one million' from the two factors. This components illustrates the top of the evidence, ending with: tan^2(x) = tan^2(x)

Answer 5

we'll do theta = x

(secx + 1) / secx
= ( (1÷cosx) + 1 ) / (1÷cosx)
= (1 + cosx)(cosx) / cosx
= 1 + cosx

On the other hand,

sin^2(x) / (1 - cosx)
= ( 1 - cos^2(x) ) / (1 - cosx)
= (1 + cosx)(1 - cosx) / (1 - cosx)
= 1 + cos x

So, as we can see both results are the same. OK

Answer 6

I assume you mean
sin²θ/(1-cosθ) = (secθ + 1)/secθ

LHS
= sin²θ/(1-cosθ)
= (1-cos²θ) / (1-cosθ)
= (1+cosθ)(1-cosθ) / (1-cosθ)
= 1 + cosθ
= 1 + 1/secθ
= (secθ+1)/secθ
= RHS