Question
Download Solution PDFWhat will be the value of cosx × cosecx - sinx × secx?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
cos x cosec x - sin x sec x
Concept used:
1. cos2x - sin2x = cos 2x
2. 2 × sinx × cosx = sin 2x
3. cot x = cos x ÷ sin x
Calculation:
cosx × cosecx - sinx × secx
⇒ \(\frac {cosx}{sinx}\) - \(\frac {sinx}{cosx}\)
⇒ \(\frac {cos^2x - sin^2x}{sinx . cosx }\)
⇒ \(2 × \frac {cos\ 2x}{2sinx . cosx}\)
⇒ \(2 × \frac {cos\ 2x}{sin\ 2x}\)
⇒ 2cot 2x
∴ The simplified value is 2cot 2x.
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