2022 · Q55
Consider the following :
- 1(tanθ +sinθ )/(tanθ -sinθ )=(secθ +1)/(secθ -1), where 0 < θ < (π)/(2). (cos²θ -sin²θ )/(cos²θ +sin²θ )=(2tanθ )/(tan²θ +1), where 0 < θ < (π)/(2).
Which of the above is/are identities?
Elementary MathematicsTrigonometry
- AOnly 1
- BOnly 2
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Statement 1: (tanθ+sinθ)/(tanθ−sinθ) = (1+cosθ)/(1−cosθ) = (secθ+1)/(secθ−1), an identity. Statement 2: the LHS is cos2θ while the RHS is 2tanθ/(1+tan²θ) = sin2θ — not identical. Only statement 1 is an identity. The keyed option is A.