Solve Homework prove that sin^2(theta)+cos^2(theta)=1

Homework Question: prove that sin^2(theta)+cos^2(theta)=1sin^2(x)+cos^2(x)=1Answer : Let ABC be a right angled triangle with an internal angle θ and a,b, c be lengths of its sides.Then we have \[sin\theta=\frac{BC}{AB}=\frac{a}{c}\] \[cos\theta=\frac{AC}{AB}=\frac{b}{c}\] Squaring and adding these two equations \[sin^2{\theta}+\cos^2{\theta}=\left(\frac{BC}{AB}\right)^2+\left(\frac{AC}{AB}\right)^2\] \[=>sin^2{\theta}+\cos^2{\theta}=\frac{a^2}{c^2}+\frac{b^2}{c^2}\] \[=>sin^2{\theta}+\cos^2{\theta}=\frac{a^2+b^2}{c^2}\] Now by…

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