Prove that (1 + cot θ -cosec θ)(1 + tan θ + sec θ) = 2

asked Mar 10, 2020 6.5k views

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Answer:

$(1+ (cos \alpha )/(sin \alpha ) - (1)/( \sin( \alpha ) ) )(1+ ( \sin( \alpha ) )/( \cos( \alpha ) )+ (1)/( \cos( \alpha ) ) )$

$(( \sin( \alpha + \cos( \alpha ) -1)/( \sin( \alpha ) )) ( ( \cos( \alpha + \sin( \alpha )+1 ) )/( cos( \alpha ) ) ) \\$

$(( \sin( \alpha + \cos( \alpha )^2)-1^2 ) )/( \sin( \alpha \cos( \alpha ) ) )$

$(sin^2@+cos^2@+2sin@cos@ -1)/(sin@cos@ ) \\$

$(1+2sin@cos@-1)/(sin@ cos@) \\$

$(2sin@cos@)/(sin@cos@) \\$

$2 \\$

hence proved

Semytech answered Mar 17, 2020

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