Prove this identity:
cos^2y - sin^2y = (1-tan^2y) / 1 + tan^2y
Please show all steps as clearly as possible as i would like to understand what exactly is going on - comments throughout the solution explaining what is going on would be greatly appreciated!!
cos^2y - sin^2y = (1-tan^2y) / 1 + tan^2y
Please show all steps as clearly as possible as i would like to understand what exactly is going on - comments throughout the solution explaining what is going on would be greatly appreciated!!
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RHS = (1-tan²y)/(1+tan²y)
Multiply numerator and denominator by cos²y
(note that tan²ycos²y = sin²y)
RHS = (1*cos²y-tan²ycos²y)/(1*cos²y+tan²ycos²y…
(cos²y - sin²y)/(cos²y +sin²y)
Since cos²y + sin²y =1
RHS = (cos²y - sin²y)/1 = LHS
Multiply numerator and denominator by cos²y
(note that tan²ycos²y = sin²y)
RHS = (1*cos²y-tan²ycos²y)/(1*cos²y+tan²ycos²y…
(cos²y - sin²y)/(cos²y +sin²y)
Since cos²y + sin²y =1
RHS = (cos²y - sin²y)/1 = LHS