What is #cottheta-sectheta+costheta# in terms of #sintheta#?

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Answer 1 · 2018-06-17T16:08:06

#2((1-sin^2theta-sintheta +(1-sin^2theta)sintheta)/(sin2theta))#

The identities used to solve this are

#1)# #sin2theta = 2sinthetacostheta#

#2)# #sin^2theta + cos^2theta = 1#

So

#=> costheta/sintheta - 1 /(costheta) + costheta#

#=> (cos^2theta-sintheta + cos^2thetasintheta)/(sinthetacostheta)#

#=> 2 ((1-sin^2theta- sintheta + (1-sin^2theta)sintheta)/(sin2theta))#