Question

Tan theta=10
Find sin(2theta)+cos(2theta)

Answer 1

Answer: B

Explanation:

`\tan \theta=10 \implies \sin \theta=(10)/(√(101)), \cos \theta=(1)/(√(101))`

`\sin 2\theta=2\sin \theta \cos \theta=2 \left((10)/(√(101)) \right)\left((1)/(√(101)) \right)=(20)/(101)`

`\cos 2\theta=2\cos^2 \theta-1=2 \left((1)/(√(101)) \right)^2 -1=-(99)/(101)`

`\therefore \sin 2\theta+\cos 2\theta=\frac{20}[101}-(99)/(101)=-(79)/(101)`