If sec theta equal to X + 1 by X prove that sec theta into tan theta equal to 2 x or 1 by 2 x
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Answer:
Its easy brother
Step-by-step explanation:
Correct question:
If sec theta =x+1/4x then prove that sec theta +tan theta =2x or 1/2x.
Solution;
Given that Secθ = x+1/4x
we know that 1+tan²θ = sec²θ
or tan²θ = (1+1/4x)²
on expanding we get
tan²θ = ( x²+1/4x)² -1
or tan²θ = ( x²+1/16x² + 1/2 -1 )
or tan²θ = (x² +1/16x² -1/2 )
or tan²θ = x² +1/16x²-1/2
or tan²θ = (x-1/4x²)
or tan²θ = (1-1/4x) or - (1-1/4x²)
when tanθ = (x-1/4x) we get
secθ+tanθ = x+1/4x + x-1/4x = 2x
when tanθ = (x-1/4x)
Secθ+tanθ = (x+1/4x) - (x-1/4x) = 1/2x
Hence
Secθ+tanθ = (x+1/4x) - (x-1/4x) = 1/2x
and secθ+tanθ = x+1/4x + x-1/4x = 2x
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