The value of sin (π/4 - cos⁻¹(-4/5)) = -7 / 5√2.
What is Trigonometry?
Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles.
Here, Sin (A - B) = Sin A Cos B - Cos A Sin B
A = π/4, B = cos⁻¹(-4/5)
Now,
sin (π/4 - cos⁻¹(-4/5)) = sin π/4 . cos(cos⁻¹(-4/5)) - cos π/4 . sin (cos⁻¹(-4/5))
sin (π/4 - cos⁻¹(-4/5)) = 1/[tex]\sqrt{2}[/tex] X (-4/5) - 1/[tex]\sqrt{2}[/tex]. sin (sin⁻¹3/5)
sin (π/4 - cos⁻¹(-4/5)) = -4/5√2 - 3/5√2
sin (π/4 - cos⁻¹(-4/5)) = -7 / 5√2.
Thus, the value of sin (π/4 - cos⁻¹(-4/5)) = -7 / 5√2.
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