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Prove that: "sec"((3pi)/2-theta)"sec"(th...

Prove that: `"sec"((3pi)/2-theta)"sec"(theta-(5pi)/2)+t a n((5pi)/2+theta)"tan"(theta-(3pi)/2)=-1.`

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We have,
LHS `=sec((3pi)/2-theta)sec(theta-(5pi)/2) + tan((5pi)/2+theta) tan(theta-(3pi)/2)`
`=-" cosec "theta sec-((5pi)/2-theta)+(-cottheta)tan-((3pi)/2-theta)`
`=-"cosec"theta("cosec"theta)+cot theta(cot theta)`
`=-"cosec"^(2)theta+cot^(2)theta=-1`=RHS
Hence proved.
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