Question
Download Solution PDFIf sec A = \(\frac{5}{4}\), then the value of \(\rm \frac{\tan A}{1 + \tan^2A} - \frac{\sin A}{\sec A}\) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
sec A = \(\frac{5}{4}\)
Concept used:
sec2θ - tan2θ = 1
sinθ.secθ = tanθ
Calculation:
\(\rm \frac{\tan A}{1 + \tan^2A} - \frac{\sin A}{\sec A}\)
⇒ \(\rm \frac{\tan A}{sec^2A} - \frac{\sin A}{\sec A}\)
⇒ \(\rm \frac{\tan A - sin\; A.sec\;A}{sec^2A}\)
⇒ \(\rm \frac{\tan A - tan\;A}{sec^2A}\)
⇒ \(\rm \frac{0}{sec^2A}\)
⇒ 0
∴ The required answer is 0.
Last updated on Jul 12, 2025
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