Question

Please solve this guys ​

Answer 1

Step-by-step explanation:

maybe this will help you.

Answer 2

Question

If cot α .cot β = 3, show that [cos (α - β)/ cos (α + β) ] = 2.

Solution

Given:-

• cot α .cot β = 3 ......(1)

To prove:-

• [cos (α - β)/ cos (α + β) ] = 2. .....(2)

Explanation

we know,

★ cos(α - β) = cos α .cosβ + sin α .sin β

★ cos(α + β) = cos α .cosβ - sin α .sin β

Take L.H.S. of equ(2)

➠ [cos (α - β)/ cos (α + β) ]

keep values by equation (1),

➠ [cos α .cosβ + sin α .sin β]/[cos α .cosβ - sin α .sin β]

divided by sin α.sin β numerator and denominator

First take numerator ,

➠ [cos α .cosβ + sin α .sin β]/[sin α.sin β]

➠ (cos α .cosβ)/(sin α.sin β) + (sin α .sin β)/(sin α.sin β)

➠ cot α .cot β + 1

Second take denominator ,

➠ (cos α .cosβ - sin α .sin β)/(sin α .sin β)

➠ (cos α .cosβ)/(sin α .sin β) - (sin α .sin β)/(sin α .sin β)

➠ cot α .cot β - 1

So,

➠ (cot α .cot β + 1)/(cot α .cot β - 1)

Keep value by equ(1)

➠ (3+1)/(3-1)

➠ 4/2

➠ 2

= R.H.S.

That's proved.

Some important formula

★ cos x / sin x = cot x

★ sin x / cos x = sin x

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