Question

If alpha and beta are two positive acute angles satisfying alpha - beta =15degree and sinalpha =cos2beta then the value of alpha + beta is equal to

Answer 1

Answer: 65°

Step-by-step explanation:

α - β = 15°                             Sin α = Cos 2β  

α = 15 + β                              Sin α  = Sin (90 - 2β)

                                            α = 90 - 2β

                                            α + 2β = 90

Now substitute the value of α

β + 15 + 2β = 90

3β = 90 - 15 = 75

β = 75/3 = 25

α = 15 + β = 25 + 15 = 40

Finally

α + β = 40 + 25 = 65°