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If sec theta = x+1/x,prove that sec theta * tan theta =2x or 1/2x

If sec theta = x+1/x,prove that sec theta * tan theta =2x or 1/2x

Grade:10

1 Answers

Arun
25758 Points
4 years ago
We realize that sec2 theta=1+tan2theta So tan2theta= (x+1/4x)2-1 On explaining we get tan2theta=(x-1/4x)2 So tan theta =(x-1/4x) or - (x-1/4x) At the point when tan theta =(x-1/4x), sec theta +tan theta= x+1/4x+ x-1/4x=2x at the point when tan theta =-(x-1/4x) sec theta +tan theta= x+1/4x-x+1/4x=1/2x

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