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प्रश्न
Prove the following:
`(cot"A"cot4"A" + 1)/(cot"A" cot4"A" - 1) = (cos3"A")/(cos5"A")`
उत्तर
L.H.S. = `(cot"A"cot4"A" + 1)/(cot"A" cot4"A" - 1)`
= `(cos"A"/(sin"A")*(cos4"A")/(sin4"A") + 1)/(cos"A"/(sin"A")*(cos4"A")/(sin4"A") - 1`
= `((cos"A"cos4"A"+sin"A"sin4"A")/(sin"A"sin4"A"))/((cos"A"cos4"A"-sin"A"sin4"A")/(sin"A"sin4"A"))`
= `(cos4"A" cos"A" + sin4"A" sin"A")/(cos4"A" cos"A" - sin4"A" sin"A")`
= `(cos(4"A" - "A"))/(cos(4"A" + "A"))`
= `(cos3"A")/(cos5"A")`
= R.H.S.
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