Question 13: Solve system of linear equations, using matrix method. 2tan¯¹ (cos x) = tan¯¹ (2 cosec x)
Class 12 - Math - Inverse Trigonometric Functions
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⇒ 2tan¯¹ (cos x) = tan¯¹ (2 cosec x)
⇒ tan¯¹ ( 2cosx / 1-cos²x ) = tan¯¹ (2 / sinx)
⇒ cos x / sin²x = 1 / sinx
⇒ cos x = sinx
⇒ cos x = sin x = π/4
∴ x = π/4
⇒ 2tan¯¹ (cos x) = tan¯¹ (2 cosec x)
⇒ tan¯¹ ( 2cosx / 1-cos²x ) = tan¯¹ (2 / sinx)
⇒ cos x / sin²x = 1 / sinx
⇒ cos x = sinx
⇒ cos x = sin x = π/4
∴ x = π/4
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