Question

If cos theta = √3/2 and theta is at acute
angle, then find 4sin^theta+tan^theta​

Answer 1

given cos teta = √3/2

WKT cos 30= √3/2

so teta = 30

then, 4sin ^ teta+ cos^ teta=4( sin^30+ tan^30)

=4(1/4+1/√3)

=4(√3+4/4√3)

=4√3+16/4√3

4√3 will be cancelled

then the answer is 16

there fore ,4 sin ^ teta+ cos^ teta= 16

Answer 2

Answer:

Value of 4sin theta +tan theta is $(2\sqrt{3}+1)/\sqrt{3}$

Step-by-step explanation:

Given;

cos theta= $\sqrt{3}/2$

As we know,

cos 30°= $\sqrt{3}/2$

∴ cos 30° = cos theta

Or, theta= 30°

Now,

4 sin theta+tan theta= 4 sin 30° +tan30°  (putting the value of theta =30°)

                                = 4×(1/2) +(1/$\sqrt{3}$)

                                = 2+(1/$\sqrt{3}$)  

                               = $(2\sqrt{3}+1)/\sqrt{3}$