Question

Prove That, Sin(45⁰-α)=cos(45⁰+α)=1/√2(cosα-sinα)

Answer 1

Answer:

refer to the attachment.

hope it helps ✨✨

Answer 2

Sin(45°-α)

= sin45°.cosα-cos45°sinα

= 1/√2.cosα- sinα.1/√2

= 1/√2(cosα-sinα) .............(i)

cos(45°+α)

= cos45°.cosα - sin45°.sinα

= 1/√2.cosα - 1/√2.sinα

= 1/√2(cosα-sinα) ..............(ii)

From (i) & (ii)

sin(45°-α) = cos(45°+α) = 1/√2(cosα-sinα).

Please Thanks This Answer❤