CBSE Class 10 Maths (Standard) 2025 · Paper 30/6/1 · Question 22(a)

Introduction to Trigonometry 2 marks Medium

a sec θ + b tan θ = m

and

b sec θ + a tan θ = n

, prove that

a^{2} + n^{2} = b^{2} + m^{2}

Answer

Squaring the given relations and subtracting, with

sec^{2} θ - tan^{2} θ = 1

, gives

m^{2} - n^{2} = a^{2} - b^{2}

, that is,

a^{2} + n^{2} = b^{2} + m^{2}

. Hence proved.

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