If \[ \frac{\sec \alpha + \tan \alpha}{\sec \alpha - \tan \alpha} = \frac{7}{4}, \] then find the value of \( \csc \alpha \).
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Given:
Let:
Then the equation becomes:
Cross-multiplying:
Expanding both sides:
Bringing all terms to one side:
Recall the identity:
Therefore:
Final Answer:
Similar Questions
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\[ \cot(A − B) = \frac{\cot A \cot B + 1}{\cot B − \cot A} \]
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Important Questions from Trigonometry
If 2 Cot x = 5, then what is (2 Cos x - Sin x) / (2 Cos x + Sin x) equal to?
For any acute angle θ, sin²θ + cos²θ = 1. Then the value of cos²θ + cos⁴θ is:
If p sin A − cos A = 1, then p2 − (1 + p2) cos A equals:
Evaluate the given expression. \[\frac{5}{1+\cot^2\theta} + \frac{3}{1+\tan^2\theta} + 2\cos^2\theta\]
Using
\[ \cot(A − B) = \frac{\cot A \cot B + 1}{\cot B − \cot A} \]
Find the value of cot 15°
