Question

If ( sin x + cos x ) = √2 cos x , Show that cot x = ( √2 + 1 ) .

Answer 1

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Answer 2

Answer :

Given that,

sinx + cosx = √2 cosx

or, (sinx + cosx)/(cosx) = √2, since cosx is non-zero

or, tanx + 1 = √2

or, tanx = √2 - 1

or, 1/(cotx) = √2 - 1, since tanx = 1/(cotx)

or, cotx = 1/(√2 - 1)

or, cotx = (√2 + 1)/{(√2 - 1)(√2 + 1)}

or, cotx = (√2 + 1)/(2 - 1)

or, cotx = √2 + 1

Therefore, cotx = √2 + 1

Hence, proved.

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