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The value of (sin(-660^@)tan(1050^@)sec(...

The value of `(sin(-660^@)tan(1050^@)sec(420^@))/(cos(225^@)cosec(315^@)cos(510^@))` is:

Text Solution

Verified by Experts

We can write the given expression as,
`(-sin(2pi-60^@)tan(3pi-30^@)sec(pi+60^@))/(cos(pi+45^@)cosec(pi-45^@)cos(3pi-30^@)`
`=(sin60^@(-tan30^@)(-sec60^@))/((-cos45^@)(cosec45^@)(-cos30^@))`
`=(sqrt3/2(-1/sqrt3)(-2))/((-1/sqrt2)(sqrt2)(-sqrt3/2))`
`=1/(sqrt3/2) = 2/sqrt3.`
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