Question 96

What is the simplified value of 1 + tan A tan (A/2) ?

Solution

1 + tan A tan (A/2)

=$$1+\dfrac{2tan(A/2)}{1-tan^{2}(A/2)}\times tan(A/2)$$

=$$\dfrac{1-tan^{2}(A/2)+2tan^{2}(A/2)}{1-tan^{2}(A/2)}$$

=$$\dfrac{1+tan^{2}(A/2)}{1-tan^{2}(A/2)}$$

=$$sec2(A/2)=secA$$

so the answer is option C.

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