Let P = [ ] : sin[ ] - cos[ ] = [ 2 , ] and Q = [ ] : sin[ ] + cos[ ] = [ 2 , ] be two set…

Question

Let P = {$$\theta $$ : sin$$\theta $$  - cos$$\theta $$ = $$\sqrt 2 \,\cos \theta $$}

and Q = {$$\theta $$ : sin$$\theta $$ + cos$$\theta $$ = $$\sqrt 2 \,\sin \theta $$} be two sets. Then

Accepted Answer

Given,

sin$$\theta $$ - cos$$\theta $$ = $$\sqrt 2 $$cos$$\theta $$

$$ \Rightarrow $$   sin$$\theta $$  = $$\left( {\sqrt 2  + 1} \right)$$cos$$\theta $$

$$ \Rightarrow $$   sin$$\theta $$ = $${{2 - 1} \over {\sqrt 2  - 1}}$$cos$$\theta $$

$$ \Rightarrow $$   $$\left( {\sqrt 2  - 1} \right)$$sin$$\theta $$ = cos$$\theta $$      . . . (1)

This is for set P.

sin$$\theta $$ + cos$$\theta $$ = $${\sqrt 2 }$$sin$$\theta $$

$$ \Rightarrow $$   cos$$\theta $$ = $$\left( {\sqrt 2  - 1} \right)$$sin$$\theta $$      . . . .(2)

This is from set Q.

So,   P = Q

Solutions · 1