Grade 11Trigonometry
sin theta+cos theta=x and sin theta-cos theta=y then prove that x**+y**=2
sin theta+cos theta=x and sin theta-cos theta=y then prove that x**+y**=2
1 Answer
Arun
Dear student
I have taken theta as @.
Now
sin@ + cos@ = x
Hence on squaring
x² = sin² @ + cos² @ + 2 sin@ * cos@
Now
y = sin@ - cos @
Hence on squaring
y² = sin²@ + cos²@ + 2sin@* cos@
Now add x² and y²
x² + y² = 2 (sin²@ + cos²@)
x² +y² = 2
Hence proved
Regards
Arun (askIITians forum expert)
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