मराठी

Prove that sec8θ-1sec4θ-1=tan8θtan2θ

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प्रश्न

Prove that `(sec8 theta - 1)/(sec4 theta - 1) = (tan8 theta)/(tan2 theta)`

बेरीज
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उत्तर

We have `(sec8 theta - 1)/(sec4 theta - 1) = ((1 - cos8 theta) cos 4theta)/(cos 8theta(1 - cos4theta))`

= `(2sin^2 4theta cos 4theta)/(cos8theta 2sin^2 2theta)`  

= `(sin4theta(2sin4theta cos 4theta))/(2cos8theta sin^2 2theta)`

= `(sin4theta sin 8theta)/(2 cos8 theta sin^2 2theta)`  

= `(2sin 2theta cos 2theta sin 8theta)/(2 cos8theta sin^2 2theta)`

= `(tan8 theta)/(tan 2theta)`  

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पाठ 3: Trigonometric Functions - Solved Examples [पृष्ठ ४१]

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एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
पाठ 3 Trigonometric Functions
Solved Examples | Q 6 | पृष्ठ ४१

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