Question 143

What is the simplified value of $$\ \frac{7}{sec^{2} \theta}+ \frac{3}{1+cot^{2} \theta}+ 4\ sin^{2} \theta$$?

Solution

Expression : $$\ \frac{7}{sec^{2} \theta}+ \frac{3}{1+cot^{2} \theta}+ 4\ sin^{2} \theta$$

= $$7cos^2\ \theta+\frac{3}{cosec^2\ \theta}+4sin^2\ \theta$$

= $$7cos^2\ \theta+3sin^2\ \theta+4sin^2\ \theta$$

= $$7cos^2\ \theta+7sin^2\ \theta$$

= $$7(cos^2\ \theta+sin^2\ \theta)$$

= $$7\times1=7$$

=> Ans - (D)

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