Question 6 of 18intermediate🔧 ApplyNumerical2 marks

If cot θ=78\theta = \frac{7}{8}, evaluate: (i) (1+sin⁡θ)(1−sin⁡θ)(1+cos⁡θ)(1−cos⁡θ)\frac{(1 + \sin \theta)(1 - \sin \theta)}{(1 + \cos \theta)(1 - \cos \theta)} (ii) cot⁡2θ\cot^2 \theta

(i)
Answer

4964\frac{49}{64}

(ii)
Answer

4964\frac{49}{64}

Explanation

This question tests the application of trigonometric identities. For part (i), we simplify the expression using the algebraic identity (a+b)(a-b) = a² - b², followed by the fundamental trigonometric identity sin²θ + cos²θ = 1. The expression simplifies directly to cot²θ. For part (ii), we simply square the given value of cot θ. Both parts yield the same numerical result.

PreviousNext