Prove that:
Sin(45°+A) + cos(45°+A) =√2 cosA
Answer:


You need to understand the given formulas to be able to solve such types of Trigonometric values of compound angles questions and answers.


Solution:

Taking LHS

= sin(45°+A) +cos(45°+A)

= sin45°.cosA +cos45°.sinA + cos45°.cosA -sin45°.sinA

= $\frac{1}{√2}$.cosA +$\frac{1}{√2}$.sinA +$\frac{1}{√2}$.cosA -$\frac{1}{√2}$.sinA

= $\frac{1}{√2}$.cosA + $\frac{1}{√2}$.cosA

= $\frac{cosA +cosA}{√2}$

= $\frac{2cosA}{√2}$

= √2 cosA

= RHS

#proved






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