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If cos 2 x − sin 2 x = tan 2 Y , Then prove that cos 2 Y − sin 2 Y = tan 2 X

If  cos2   x  − sin2  x  =  tan2 Y  , Then prove that
cos2 Y  − sin2 Y = tan X

Grade:11

2 Answers

Arun
25763 Points
3 years ago

cos²x-sin²x=sec²y-1

cos²x+1-sin²x=sec²y

2cos²x=sec²y

2/sec²y=1/cos²x

sec²x=2 cos²y

1+tan²x=2cos²y

tan²x=2cos²y-1

tan²x=cos²-sin²y

Susmita
425 Points
3 years ago
\frac{cos^2 x-sin^2 x}{1}=\frac{sin^2 y}{cos^2 y}
\frac{cos^2 x-sin^2 x+1}{cos^2 x -sin^2 x -1}=\frac{sin^2 y +cos^2 y}{sin^2 y-cos^2 y}
\frac{cos^2 x-sin^2 x+(cos^2 x+ sin^2 x)}{cos^2 x -sin^2 x -(cos^2 x+sin^2 x)}=\frac{1}{sin^2 y-cos^2 y}
\frac{2cos^2 x}{-2sin^2 x}=\frac{1}{sin^2 y-cos^2 y}
Rearrange and you will get the ans.Please approve if helped.............................................................................................................
 
 

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