The value of sin2 θ cos2 θ ( sec2 θ + cosec2 θ) is(a) 2 (b) 4 (c

1.	The value of sin2 θ cos2 θ ( sec2 θ + cosec2 θ) is(a) 2 (b) 4 (c) 1 (d) 3
Answer» (c) 1 sin² θ cos² θ (sec² θ + cosec² θ) = sin² θ cos² θ \(\bigg(\frac{1}{cos^2\,\theta}+\frac{1}{sin^2\,\theta}\bigg)\) = sin² θ cos² θ \(\bigg(\frac{sin^2\,\theta\,+\,cos^2\,\theta}{cos^2\,\theta\,sin^2\,\theta}\bigg)\) = sin² θ + cos² θ = 1

The value of sin2 θ cos2 θ ( sec2 θ + cosec2 θ) is(a) 2 (b) 4 (c) 1 (d) 3

Answer»

(c) 1

sin² θ cos² θ (sec² θ + cosec² θ)

= sin² θ cos² θ \(\bigg(\frac{1}{cos^2\,\theta}+\frac{1}{sin^2\,\theta}\bigg)\)

= sin² θ cos² θ \(\bigg(\frac{sin^2\,\theta\,+\,cos^2\,\theta}{cos^2\,\theta\,sin^2\,\theta}\bigg)\)

= sin² θ + cos² θ = 1