How to verify Trigonometric Identities?
To proof and verify the identities we will make use of the basic trigonometric identities to make sure that both the sides of the equation is equal to each other.
1. If tan A = (sin θ
- cos θ)/(sin θ + cos θ) then prove that,
sin θ + cos θ = ± √2 cos A
Solution:
We know that, sec2 A = 1 + tan2 ANow taking square root on both the sides we get,
sin θ + cos θ = ± √2 cos A .
Proved
More examples to get the basic ideas to proof and verify Trigonometric Identities.
Proved
cosαx=sinα2y=√cos2α+sin2αx2+4y2=1x2+4y2
Therefore,cosθ=xx2+4y2andsinθ=2yx2+4y2
Now, 2x sec α - y csc α = 3
⇒ 2x ∙ 1cosα - y ∙ 1sinα = 3, [Since, sec α = 1cosα and csc α = 1sinα]
⇒ 2x ∙ √x2+4y2x - y ∙ √x2+4y22y = 3, [putting the values of sin α and cos α]
⇒ 32√x2+4y2=3
⇒ √x2+4y2=2
Now taking square root on both the sides
we get,
Proved
Note: Remember there is no set method that can be applied to verify trigonometric identities. However, a few different techniques needed to follow to start verifying from one side, based on the identity which is to be verified.
● Trigonometric Functions
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