Question

Sin10°×sin50°×sin70°​

Answer 1

sin10°sin50°sin70°.

=sin10° cos(90∘−50°)cos(90∘−70°).

=2sin10∘cos10∘cos40∘cos20∘/2cos10

=2sin20∘cos20∘cos40/4 cos10

=2sin40∘cos40/8cos10∘.

=sin80/8cos10∘

=cos10/8cos10

=1/8.

Answer 2

To calculate the value of sin(10°) × sin(50°) × sin(70°), you can use the trigonometric identity:

sin(a) × sin(b) × sin(c) = (1/4) × [cos(a - b - c) - cos(a + b - c) - cos(a - b + c) + cos(a + b + c)]

Plugging in the values, we have:

sin(10°) × sin(50°) × sin(70°) = (1/4) × [cos(10° - 50° - 70°) - cos(10° + 50° - 70°) - cos(10° - 50° + 70°) + cos(10° + 50° + 70°)]

Simplifying further:

sin(10°) × sin(50°) × sin(70°) = (1/4) × [cos(-110°) - cos(-10°) - cos(30°) + cos(130°)]

Since cos(-x) = cos(x), we can rewrite the expression as:

sin(10°) × sin(50°) × sin(70°) = (1/4) × [cos(110°) - cos(10°) - cos(30°) + cos(130°)]

Now we can evaluate the cosines:

cos(110°) ≈ -0.342 cos(10°) ≈ 0.985 cos(30°) ≈ 0.866 cos(130°) ≈ -0.342

Substituting the values back into the expression:

sin(10°) × sin(50°) × sin(70°) ≈ (1/4) × [-0.342 - 0.985 - 0.866 + (-0.342)]

Calculating the result:

sin(10°) × sin(50°) × sin(70°) ≈ (1/4) × [-2.535]

Finally:

sin(10°) × sin(50°) × sin(70°) ≈ -0.634