The expression sin
2
θ+cos
2
θ−1=0 is satisfied by how many values of θ?
- ANo value
- BOnly one value
- CInfinitely many values
- DTwo values
Solution & Step-by-step Explanation
The given expression is:
sin
2
θ+cos
2
θ−1=0
Rearranging the expression, we get:
sin
2
θ+cos
2
θ=1
According to standard trigonometric identities, sin
2
θ+cos
2
θ=1 is a fundamental identity that holds true for all real values of θ.
Since it is true for every real value of θ, there are infinitely many values that satisfy the expression.
sin
2
θ+cos
2
θ−1=0
Rearranging the expression, we get:
sin
2
θ+cos
2
θ=1
According to standard trigonometric identities, sin
2
θ+cos
2
θ=1 is a fundamental identity that holds true for all real values of θ.
Since it is true for every real value of θ, there are infinitely many values that satisfy the expression.