Question

cosec^2(60°)tan37°+ tan^3(30°)cos30°-sec 53° sin 37°+ tan30° sin60° sec 53° = sin3x​

Answer 1

Given: cosec²(60°)tan37°+ tan³(30°)cos30°-sec 53° sin 37°+ tan30° sin60° sec 53° = sin3x​

To find: Value of x = ?

Solution:

• Now we have the general values/ trigonometric values of some common terms:

             sin 37° = 3/5

             cos 37° = 4/5

             sin 53° = 4/5

             cos 53° = 3/5

             tan 37° = 3/4

             tan 53° = 4/3

• Now we can put these values in the LHS side and find out the value, we get:

             (2/√3)² x 3/4 + (1/√3)³ x (√3/2) - 5/3 x 4/5 + 1/√3 x √3/2 x 5/3

             1 + 1/6 - 4/3 + 5/6

             12/6 - 4/3

             4/6

• Now, sin 3x = 2/3

                  3x = sin^-1 (2/3)

                   x = 1/3(sin^-1 (2/3))

Answer:

         The value of x is 1/3(sin^-1 (2/3)).