Question 145
What is the simplified value of$$\ \frac{3}{cosec^{2}\theta}+\frac{5}{1+tan^{2}\theta}-2cos^{2}\theta$$?
Solution
Expression = $$\ \frac{3}{cosec^{2}\theta}+\frac{5}{1+tan^{2}\theta}-2cos^{2}\theta$$
= $$3sin^{2}\theta+\frac{5}{sec^{2}\theta}-2cos^{2}\theta$$
= $$3sin^{2}\theta+5cos^{2}\theta-2cos^{2}\theta$$
= $$3sin^{2}\theta+3cos^{2}\theta$$
= $$3(sin^{2}\theta+cos^{2}\theta)$$
= $$3\times1=3$$
=> Ans - (A)
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