Question

Q32) If cose + sino = 1, prove that cose - sino = +1.​

Answer 1

$\huge\mathcal{\underline{\underline{Solution}}}$

cos∅ + sin∅ = 1

Prove that :-

cos∅ - sin∅ = ±1

According to questions :-

cos∅ + sin∅ = 1

squaring both sides :-

(sin∅ + cos∅)² = 1

sin²∅ + cos²∅ + 2sin∅.cos∅ = 1

[°•° sin²∅ + cos²∅ = 1 ]

1 + 2sin∅.cos∅ = 1

2sin∅ .cos∅ = 1 - 1

sin∅.cos∅ = 0 -------->(1)eq.

Again,

(sin∅ - cos∅)² = 1 - 2sin∅.cos∅

(sin∅ - cos∅)² =1 - 2 × 0

(sin∅ - cos∅)² = 1

•°• sin∅ - cos∅ = ±1

Hence proved