Question 76

Find$$ (1 - cos^{2}\theta )(cot^{2}\theta + 1) - 1$$.

Solution

${sin^2(} θ) + {cos^}^{2(} θ) = 1$

$1 + {cot^}^{2(} θ) = {cosec^}^{2(} θ)$

${(sin^}^{2(} θ) + {cos^}^{2(} θ) = 1)$

${(sin^}^{2(} θ) = 1 - {cos^}^{2(} θ))$

Now let's substitute:

$((1 - {cos^}^{2(} θ)) (1 + {cot^}^{2(} θ))-1$

$(({sin^}^{2(} θ)) ({cosec^}^{2(} θ)))-1$

The relationship between sin and cosec is:

$cosec = \frac{1}{sin}$

thus

${cosec^}^{2(} θ) = \frac{1}{{sin^}^{2(} θ)}$

and so ( $({sin^}^{2(} θ)) (\frac{1}{{sin^}^{2(} θ)}))-1 = 1-1 = 0$

Get AI Help

Create a FREE account and get:

Download RRB Study Material PDF
45+ RRB previous papers with solutions PDF
300+ Online RRB Tests for Free

maruti sir image

Join CAT 2026 course by 5-Time CAT 100%iler

Crack CAT 2026 & Other Exams with Cracku!

Enroll Now

cracku download image

Ask our AI anything

AI can make mistakes. Please verify important information.