If 2 tan - 1 ⁡ cos ⁡ x = tan - 1 ⁡ ( 2 cosce ⁡ x ) t h e n sin ⁡ x + cos ⁡ x =

Question

If 2 tan - 1 ⁡ cos ⁡ x = tan - 1 ⁡ ( 2 cosce ⁡ x ) t h e n sin ⁡ x + cos ⁡ x =, 2 2, 2, 1 2, 1 2

MARKS App · Accepted Answer

As given, 2 tan - 1 ⁡ cos ⁡ x = tan - 1 ⁡ ( 2 cosce ⁡ x ) tan - 1 ⁡ cos ⁡ x + tan - 1 ⁡ cos ⁡ x = tan - 1 ⁡ ( 2 cosce ⁡ x ) Since cos x ≤ 1 = tan - 1 ⁡ 2 cos ⁡ x 1 - cos 2 ⁡ x = tan - 1 ⁡ ( 2 cosce ⁡ x ) ⇒ 2 cos ⁡ x sin 2 ⁡ x = 2 cosce ⁡ x ⇒ 2 cot ⁡ x = 2 ⇒ cot ⁡ x = 1 ⇒ x = π 4 Hence, sin ⁡ x + cos ⁡ x = sin ⁡ π 4 + cos ⁡ π 4 = 1 2 + 1 2 = 2

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