sin²theta + cos² theta = 1
prove the trigonometric identities
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Answered by
6
Answer:
Let ABC be a right angled triangle right angled at B.
Let angle C ie angle ACB = theeta.
Now by Pythagoras theorem
AC^2= AB^2+BC^2 ……(1)
We know that sin theta = opposite side/ hypotenuse.
So sin theta = AB/AC. Similarly
cos theta= adjacent side/ hypotenuse
So cos theta = BC/AC
Now sin^2 theta + cos^2 theeta
= (AB/AC)^2 + (BC/AC)^2
= AB^2/AC^2 + BC^2/AC^2
= (AB^2+BC^2)/AC^2
= AC^2/AC^2 = 1 ( by using (1) )
Step-by-step explanation:
Answered by
53
let PQR a right angle triangle
and right angled at R.
and angle θ at P.
By Pythagoras theorem
So ,
Now, Squaring Both Sides
Similarly,
Squaring Both Sides
Now Adding cos² θ and sin² θ
So,
we know that
By Pythagoras theorem
So, we Substitute the value of pr²+qr² In eq(1)
Now,
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