How do you simplify #5sec2theta-csc2theta# to trigonometric functions of a unit #theta#?

1 Answer
Shwetank Mauria
Apr 5, 2018

#5sec2theta-csc2theta=(10sinthetacostheta-2cos^2theta+1)/(4sinthetacos^3theta-2sinthetacostheta)#

Explanation:

We can use #sin2theta=2sinthetacostheta# and #cos2theta=2cos^2theta-1#

Hence #5sec2theta-csc2theta#

= #5/(cos2theta)-1/(sin2theta)#

= #(5sin2theta-cos2theta)/(sin2thetacos2theta)#

= #(10sinthetacostheta-2cos^2theta+1)/(2sinthetacostheta(2cos^2theta-1))#

= #(10sinthetacostheta-2cos^2theta+1)/(4sinthetacos^3theta-2sinthetacostheta)#

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