Question

Find the value of theta if sin^2 theta =1-cos^2 theta

Answer 1

Hey friend,here's the solution to Ur problem:

sin2theta= 1-cos2theta
or,2sin theta×cos theta = 1-(1-2sin^2 theta)
or,2sin theta×cos theta = 1-1+2sin^2theta
or,2sin theta×cos theta = 2sin^2 theta
on dividing both sides by 2 sin theta, we get
,cos theta= sin theta
or,cos theta/cos theta= sin theta/ cos theta --------{dividing both sides by cos theta}
or,1 = tan theta
or,tan 45°=tan theta
or,45°= theta
Therefore,theta= 45°.

Answer 2

There is no unique value of theta that satisfies the equation. The equation is true for all values of theta.

Given:

sin^2 theta =1-cos^2 theta

To find:

The value of theta that satisfies the equation.

Solution:

The equation that we are given is

sin^2 theta = 1 - cos^2 theta.

This equation can be rewritten as

sin^2 theta + cos^2 theta = 1.

Recall that the sum of the squares of the sine and cosine functions is equal to 1, so this equation is always true for any value of theta. This means that there is no unique value of theta that satisfies the given equation. Instead, the equation is true for all values of theta. In other words, the equation holds for an infinite number of values of theta. This is because the sine and cosine functions repeat over a period of 360 degrees (or 2*pi radians).

So there are an infinite number of possible values for theta that will make the equation hold. This is why we say that there is no unique value of theta that satisfies the equation

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