Question

Prove that → cosθ + sinθ = √2cosθ.

#Mathematics

#Trigonometry

Answer 1

Hello !
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Your statement seems incomplete : 

It should be like this :

If cosФ -  sinФ = √2 sinФ . Prove that :
   cosФ + sinФ = √2 cosФ.
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Solution : 
here, cosФ -  sinФ     = √2 sinФ ____________(1)

         sinФ + √2 sinФ = cosФ

         sinФ(1+√2)       = cosФ 

         sinФ                 = cosФ x 1/(1+√2)

         sinФ                 = cosФ x 1/(1+√2) x √2-1/√2-1

         sinФ                 = cosФ x (√2-1) /(2-1)

         sinФ                 =  (√2-1)cosФ

         sinФ                 = √2 cosФ - cosФ

         sinФ + cosФ    = √2 cosФ
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Answer 2

Step-by-step explanation:

Hello !

______________________________________________________

Your statement seems incomplete :

It should be like this :

If cosФ - sinФ = √2 sinФ . Prove that :

cosФ + sinФ = √2 cosФ.

______________________________________________________

Solution :

here, cosФ - sinФ = √2 sinФ ____________(1)

sinФ + √2 sinФ = cosФ

sinФ(1+√2) = cosФ

sinФ = cosФ x 1/(1+√2)

sinФ = cosФ x 1/(1+√2) x √2-1/√2-1

sinФ = cosФ x (√2-1) /(2-1)

sinФ = (√2-1)cosФ

sinФ = √2 cosФ - cosФ

sinФ + cosФ = √2 cosФ

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