Question

if sin(x-20°)= cos(3x-10°) then find value of x​

Answer 1

Step-by-step explanation:

Given :-

sin(x-20°)= cos(3x-10°)

To find :-

Find the value of x ?

Solution :-

Method-1:-

Given that :

Sin(x-20°)= Cos(3x-10°)

=> Sin (90°-(110°-x)) = Cos (3x-10°)

We know that

Sin (90°-A) = Cos A

=> Cos (110°-x) = Cos (3x-10°)

=> 110°-x = 3x-10°

=> 110°+10° = 3x+x

=> 120° = 4x

=> 4x = 120°

=> x = 120°/4

=> x = 30°

Therefore, x = 30°

Method -2:-

Given that :

Sin(x-20°)= Cos(3x-10°)

=> Sin (x-20°) = Cos (90-(100°-3x))

We know that

Cos (90°-A) = Sin A

=> Sin (x-20°) = Sin (100°-3x)

=> x-20° = 100° -3x

=> x+3x = 100°+20°

=> 4x = 120°

=> x = 120°/4

=>x = 30°

Therefore, x = 30°

Answer:-

The value of x for the given problem is 30°

Check:-

If x = 30° then LHS = Sin (x-20°)

=> Sin (30°-20°)

=> Sin 10°

=> Sin (90°-80°)

=> Cos 80° -------(1)

and RHS = Cos (3x-10°)

=> Cos (3(30°)-10°

=> Cos (90°-10°)

=> Cos 80°--------(2)

From (1) & (2)

LHS = RHS is true for x = 30°

Used formulae :-

• Cos (90°-A) = Sin A

• Sin (90°-A) = Cos A

Answer 2

x=30°

hope it helps you ✌ friend