Question

if tan theta = 1/2 prove that sin 2theta + 2 cos 2 theta = 2​

Answer 1

Answer:

Step-by-step explanation:

Given that,

Tan A=(1/2)

To prove: Sin2A+2cos2A=2

Now , tanA=1/2=p/b

Therefore,h=√1+4=√5

Hence sinA =(p/h)=1/√5 & CosA=(b/h)=2/√5

Now,LHS=Sin2A+2cos2A

= 2 sinAcosA+2(1-2sin^2A)

=2 (1/√5)(2/√5)+2{1-2 (1/5)}

=2(2/5)+2{(5-2)/5}

=4/5+6/5

=(4+6)/5=10/5=2=RHS