Example 10 - Chapter 2 Class 12 Inverse Trigonometric Functions

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Example 10 Show that sin-1 3/5 sin-1 8/17 = cos-1 84/85 Let sin-1 3/5 = a and sin-1 8/17 = b We know that cos (a b) = cos a cos b + sin a sin b cos (a b) = 4/5 15/17 + 3/5 8/17 cos (a b) = (60 + 24)/(17 5) cos (a b) = 84/85 (a b) = cos-1 (84/85) Putting the value of a and b sin-1 3/5 sin-1 8/7 = cos-1 (84/85) Hence proved