Question

if 20sin a=15 sinb=12 prove that 4cos a+3cos b= -5​

Answer 1

Step-by-step explanation:

tan 70 -tan 20 -2 tan 40 = 4 tan 10 (to be proved)

now,

lhs,

=(tan 70 – tan 40 ) – (tan 40 + tan 20)

=(sin 70 /cos 70 – sin 40/ cos 40 ) – (sin 40 / cos 40 + sin 20 / cos 20)

=sin 30 /(cos 70 *cos 40) – sin 60 / (cos 20 * cos 40 )

=1/ 2 cos 40 *(1/cos 70 – sqrt 3 /cos 20)

=1/cos 40 *(1/2*cos 20 -sqrt 3*sn 20 /2)/(sin 20* cos 20)

=2/cos 40 *(cos 60* cos 20 -sin 60 * sin 20 )/(2 sin 20 *cos 20)

=2/ cos 40 *(cos 80/ sin 40)

=4 *(cos 80/ 2 cos 40* sin 40)

=4*(cos 80 /sin 80)

=4 cot 80

=4 cot (90-10

=4 tan 10

hence, proved.

Hope it helps☺

Make me a brainlest if u wish