Question

If a and 2a-45 are acute angles such that sin a = cos(2a-45) then tan a =?

Answer 1

Answer:

1

Step-by-step explanation:

SinA = Cos(2A-45)

Cos(90-A) = Cos(2A-45) (∵ Cos(90-θ) = Sinθ)

=> 90-A = 2A - 45

=> 2A + A = 90 + 45

=> 3A = 135°

=> A = 45°

Now TanA = Tan45° = 1.

Answer 2

GIVEN

a and 2a-45 is an acute angle , sin a= cos( 2a-45)

TO FIND

the value of tan a=?

SOLUTION

we are given,

sinA= cos(2A-45)

we will change sin to cos, it is converted by 90-A

⇒cos (90-A) = cos (2A-45)

since we have cos on both sides, we cancel cos,

⇒(90-A) = (2A-45)

solving the expression to find the value of A,

⇒90+45 =2A+A

evaluating,

⇒ 135 = 3A

⇒ A= $\frac{135}{3}$

A=45°

NOW we require to find the value of tan A,

replacing the value of A,

tan 45°= 1 ( by table)

HENCE THE VALUE OF Tan A= Tan 45°= 1.