UPSKILL MATH PLUS

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1. The value of \(sin^2 \ \theta + \frac{1}{1 + tan^2 \ \theta}\) is equal to
 
2. \(tan \ \theta \ cosec^2 \ \theta - tan \ \theta\) is equal to
 
3. If \((sin \ \alpha + cosec \ \alpha)^2 + (cos \ \alpha + sec \ \alpha)^2 = k + tan^2 \ \alpha + cot^2 \ \alpha\), then the value of \(k\) is equal to
 
4. If \(sin \ \theta + cos \ \theta = a\) and \(sec \ \theta + cosec \ \theta = b\), then the value of \(b(a^2 - 1)\) is equal to
 
5. If \(5x = sec \ \theta\) and \(\frac{5}{x} = tan \ \theta\), then \(x^2 - \frac{1}{x^2}\) is equal to