Question

What is the value of cot 70° + 4 cos 70° ?

(a) 1/✓3
(b) ✓3

Answer 1

hi friend here is ur answer hope this will help you.


LHS=cot700+4cos700LHS=cot⁡700+4cos⁡700

=cos700+4cos700sin700sin700=cos⁡700+4cos⁡700sin⁡700sin⁡700

=cos700+2sin1400sin700=cos⁡700+2sin⁡1400sin⁡700

=cos700+2sin400sin700=cos⁡700+2sin⁡400sin⁡700

=cos700+2cos500sin700=cos⁡700+2cos⁡500sin⁡700

=cos700+cos500+cos500sin700=cos⁡700+cos⁡500+cos⁡500sin⁡700

=2cos600cos100+cos500sin700=2cos⁡600cos⁡100+cos⁡500sin⁡700

=cos100+cos500sin700=cos⁡100+cos⁡500sin⁡700

=2cos300cos200sin700=2cos⁡300cos⁡200sin⁡700

=2cos300sin700sin700=2cos⁡300sin⁡700sin⁡700

=2cos300=2cos⁡300

=3–√

Answer 2

Hey

Here is your answer,

To find : cot 70° + 4 cos 70°

Solution :

L.H.S= cos 70/sin 70+4 cos 70
= cos 70+4 cos 70 sin 70/sin 70
=cos 70+2 sin 40/sin 70
= cos 70+2 cos 50/sin 70
= cos 70+cos 50+cos 50/sin 70
= 2 cos 60 cos 10+cos 50/sin 70
= cos 10+cos 50/sin 70
= 2 cos 30 cos 20 /cos 20
= root 3

Hope it helps you!