3) prove the following
(Trigonometric identities)
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3) prove the following
(Trigonometric identities)
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In both of them ypu can just cross multiply.
And the resultant is a known identity for being equal to 1.
=> cosec x - cot x = 1 / (cosec x + cot x)
=> (cosec x - cot x)(cosec x + cot x) = 1
=> cosec ² x - cot ² x = 1 {known to be equal to one}
=> 1 = 1 Hence Proved.
The same can be done for the other one and be rearranged.
cross multiplying you'll get
=> (cosec x + 1)(cosex - 1) = cot x * cot x
=> cosex ² x - 1 = cot ² x
=> cosec ² x - cot ² x = 1
=> 1 = 1 Hence Proved.