what's the value of cos^2(80°+theta)+sin^2(100°-theta)?
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100-Φ = 180-(80+Φ) ,it can be ritten like this
sin(100-Φ) = sin(180-(80+Φ))
sin(100-Φ) = sin(80+Φ) [sin(180-Φ)=sinΦ]
so replacing this in the given question we get
cos^2(80+Φ) + sin^2(80+Φ) = 1
which is nothing but sin^2Φ+cos^2Φ =1
hence the answer is 1
sin(100-Φ) = sin(180-(80+Φ))
sin(100-Φ) = sin(80+Φ) [sin(180-Φ)=sinΦ]
so replacing this in the given question we get
cos^2(80+Φ) + sin^2(80+Φ) = 1
which is nothing but sin^2Φ+cos^2Φ =1
hence the answer is 1
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