Question

if sin6x = cos3x then what is the value of x
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Answer 1

Step-by-step explanation:

Given:-

Sin6X = Cos3X

To find:-

Find the value of X?

Solution:-

Method-1:-

Given that

Sin6X = Cos3X

We know that Sin A = Cos (90°-A)

=> Cos (90° - 6X ) = Cos 3X

=>90° - 6X = 3X

=>90° = 3X + 6X

=>90° = 9X

=>9X = 90°

=>X = 90°/9

=>X = 10°

Method -2:-

Given that

Sin6X = Cos3X

We know that Cos A = Sin (90°-A)

=> Sin 6X = Sin (90° - 3X)

=> 6X = 90° - 3X

=>6X +3X = 90°

=>9X = 90°

=>X = 90°/9

=>X = 10°

Answer:-

The value of X for the given problem is 10°

Check:-

If X = 10°

LHS = Sin (6×10°)=Sin 60° = √3/2

RHS = Cos (3×10°)=Cos 30° = √3/2

LHS = RHS is true for X = 10°

Used formulae:-

• Cos A = Sin (90°-A)
• Sin A = Cos (90°-A)
• Sin 60° = √3/2
• Cos 30° = √3/2