Question

If sin theta= 2/5 , then find the value of 4+4tan² theta.

Answer 1

100/21 is the answer

Answer 2

sin theta=2/5
sin square theta=4/25
1-cos square theta=4/25                {using identity:sin^2 Theta=1-cos^2 theta}
cos^2 theta=1-4/25
cos^2 theta=21/25
sec^2 theta=25/21

   4+4 tan^2 theta
=4[1+tan^2 theta]
=4 sec^2theta                                   {using identity:1+tan^2=Sec^2}
=4*25/21
=100/21


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