# If Cos θ + Cot θ = M and Cosec θ – Cot θ = N, Prove that Mn = 1 - Mathematics

If cos θ + cot θ = m and cosec θ – cot θ = n, prove that mn = 1

#### Solution

LHS = mn

= (cosec theta + cot theta) (cosec theta - cot theta)

= cosece^2 theta - cot^2 theta

= 1    [∵ (1 + b)(a - b) = a^2 - b^2 cosec^2 theta - cot^2 theta = 1]

=RHS

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Exercise 11.1 | Q 81 | Page 47