The value of the given expression is 2√10 / 7.
What is trigonometric identity?
Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.
Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence. These are identities that, geometrically speaking, involve certain functions of one or more angles.
Solve cos(sin⁻¹(3/7)). Break it into simpler terms sin⁻¹(3/7) these will be taken as an angle when dealing with cos.
sin Ф = opposite / hypothenus = 3/7
Using Pythagoras Theorem
Hypothesis ² = opposite² + adjacent ²
7² = 3² + a²
49 = 9 + a²
a² = 49 - 9 = 40
a = √40 = √2x2x10 = 2√10
cos Ф = adjacent / hypothenus = 2√10 / 7
cos(sin⁻¹(3/7)) = 2√10 / 7
Hence, the value of cos(sin⁻¹(3/7)) will be 2√10 / 7.
To know more about Trigonometry follow
https://brainly.com/question/24349828
#SPJ2
