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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.`

Text Solution

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`sec((3pi)/2-theta)sec(theta-(5pi)/2)+tan((5pi)/2+0)tan(theta-(3pi)/2)`
`=-cosecthetacosectheta+cotthetacot theta`
`=-(cosec^2theta-cot^2theta)=-1`
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Knowledge Check

  • tan(pi/4 + theta) tan (pi/4 -theta)=

    A
    0
    B
    `1/sqrt3`
    C
    1
    D
    `sqrt3`

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