Question

what are the trigonometrical identities explain with examples

Answer 1

Trigonometric identities are equations involving the trigonometric functions that are true for every value of the variables involved.

Some of the most commonly used trigonometric identities are derived from thePythagorean Theorem , like the following:

sin 2 ( x ) + cos 2 ( x ) = 1 1 + tan 2 ( x ) = sec 2( x ) 1 + cot 2 ( x ) = csc 2 ( x )

Example 1:

Simplify the expression using trigonometric identities.

1 − sin 2 ( θ ) tan 2 ( θ )

Rewrite tan as sin / cos .

= 1 − sin 2 ( θ ) ( sin 2 ( θ ) cos 2 ( θ ) ) = 1 −sin 2 ( θ ) ⋅ cos 2 ( θ ) sin 2 ( θ ) = 1 − cos 2 ( θ)

Use the fundamental Pythagorean identity, we get

= sin 2 ( θ )

Hope u like the ans... Plse Mark me as brainlist

Answer 2

Hi,

Your answer :
These identities are useful for simplifying and solving problems.
Their proofs are given below.
Based on the right angle triangle (right triangle) in the figure beside, sin A = a / b and cos A = c / b.
Thus sin2 A + cos2 A = (a2 + c2) / b2.
According to the Pythagorean Theorem, a2 + c2 = b2 in a right triangle.
Thus sin2 A + cos2 A = 1 and equation (1) is proved.
 
Dividing the two sides of equation (1) by cos2 A,
We get tan2 A + 1 = 1 / cos2 A = sec2 A. Equation (2) is proved.
 
Dividing the two sides of equation (1) by sin2 A,
We get 1 + cot2 A = 1 / sin2 A = cosec2 A. Equation (3) is proved.

Good bye :)