Question

Let tan(80°) = k . Find the value of (√3)cos(20°)+cos(70°) in term of k.

Answer 1

Answer:

2/√(1 + k²)

Step-by-step explanation:

we have

sin 80° = sin ( 60° + 20° ) = (√3/2)cos(20°)+ 1/2cos(70°)

2sin 80° = (√3)cos(20°)+cos(70°)

there fore

(√3)cos(20°)+cos(70°)  = 2sin 80°

                                      = 2/sec 80°  = 2 / √sec² 80° = 2 / √( 1 + tan² 80° )

                                       = 2/√(1 + k²)