Question

(sin^2theta+cos^2theta)​

Answer 1

Answer:

2sin( theta) cos(theta)

Answer 2

Solution :-

★ sin²θ + cos²θ = 1 ★

Reason :- It is first trigonometric identity

Proof :-

Let the base of ∆ be x

Let the height of the ∆ be y

Now , finding the hypotenuse of the ∆ using Pythagoras theorem

Hypotenuse² = Base² + Height²

Hypotenuse = x² + y²

Now, proving that sin²A + cos²A = 1

sinA = opposite/Hypotenuse

Squaring on both sides

sin²A = opposite²/Hypotenuse² = x²/x² + y²

cosA = adjacent/Hypotenuse

cos²A = adjacent²/Hypotenuse² = y²/x² + y²

Now, adding sin²A & cos²A

sin²A + cos²A = x²/x² + y² + y²/x² + y²

sin²A + cos²A = (x² + y²)/(x² + y²)

sin²A + cos²A = 1

Hence , proved !

Trigonometric identities :-

1st identity :- sin²A + cos²A = 1

2nd identity :- sec²A - tan²A = 1

3rd identity :- cosec²A - cot²A = 1