NDA2019MathematicsTrigonometric Ratios & IdentitiesActual
Paragraph: It is given that ( - )=a, ( - )=b Question: What is ^2( - )+2 a b ( - ) equal to?
Options
- Aa^2+b^2
- Ba^2-b^2
- Cb ^2- a ^2
- D- (a^2+b^2 )
Correct answer
A. a^2+b^2
Step-by-step solution
^2( - )+2 ab ( - )=1- ^2( - )+2 ab aligned & ( - )=1- ( - )[ ( - )-2 ab ] & = 1- (a b+ 1-a^2 1-b^2 ) [a b+ 1-a^2 1-b^2 -2 a b ] &= 1- ( 1-a^2 1-b^2 +a b ) ( 1-a^2 1-b^2 -a b ) &= 1- [ ( 1-a^2 1-b^2 )^2-(a b)^2 ] aligned aligned & =1- [ (1-a^2 ) (1-b^2 )-a^2 b^2 ) & =1- (1-b^2-a^2+a^2 b^2-a^2 b^2 ) & =1-1+b^2+a^2=a^2+b^2 aligned