How do you verify the identity $(2+cscthetasectheta)/(cscthetasectheta)=(sintheta+costheta)^2$ ?

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Answer 1 · 2016-09-01T15:39:14

You will need the following identities to prove this identity.

• $cscbeta = 1/sinbeta$

• $secbeta = 1/cosbeta$

• $sin^2beta + cos^2beta = 1$

Simplify the left-hand side and expand the right-hand side.

$(2 + 1/sintheta xx 1/costheta)/(1/sintheta xx 1/costheta) = sin^2theta+ 2sinthetacostheta + cos^2theta$

$(2 + 1/(sinthetacostheta))/(1/(sinthetacostheta)) = 1 + 2sinthetacostheta$

$((2sinthetacostheta + 1)/(sinthetacostheta))/(1/(sinthetacostheta)) = 1 + 2sinthetacostheta$

$(2sinthetacostheta+ 1)/(sin thetacostheta) xx (sinthetacostheta)/1 = 1+ 2sinthetacostheta$

$2sinthetacostheta + 1 = 1 + 2sinthetacostheta$

Identity proved!!

Hopefully this helps!

How do you verify the identity (2+cscthetasectheta)/(cscthetasectheta)=(sintheta+costheta)^2(2+cscthetasectheta)/(cscthetasectheta)=(sintheta+costheta)^2?