Question

If tan A=40/9 then verify 1-cos*2A=2sin*2A-1
prove that answer
I will mark in brainlist​

Answer 1

Given,

tan θ = 12/13 …….. (1)

We know that by definition,

tan θ = Perpendicular side opposite to ∠θ / Base side adjacent to ∠θ …… (2)

On comparing equation (1) and (2), we have

Perpendicular side opposite to ∠θ = 12

Base side adjacent to ∠θ = 13

Thus, in the triangle representing ∠ θ we have,

Hypotenuse AC is the unknown and it can be found by using Pythagoras theorem

So by applying Pythagoras theorem, we have

AC2 = 122 + 132

AC 2 = 144 + 169

AC2 = 313

⇒ AC = √313

By definition,

sin θ = Perpendicular side opposite to ∠θ / Hypotenuse = AB / AC

⇒ sin θ = 12/ √313…..(3)

And, cos θ = Base side adjacent to ∠θ / Hypotenuse = BC / AC

⇒ cos θ = 13/ √313 …..(4)

Now, substituting the value of sin θ and cos θ from equation (3) and (4) respectively in the equation below

R D Sharma Solutions For Class 10 Maths Chapter 5 Trigonometric Ratios ex 5.1 - 41

Therefore,

R D Sharma Solutions For Class 10 Maths Chapter 5 Trigonometric Ratios ex 5.1 - 42