AP EAMCET202124 Aug 2021Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual
^2 10^ + ^2 50^ - 40^ 80^ is equal to
Options
- A1 4
- B1 2
- C4 3
- D3 4
Correct answer
D. 3 4
Step-by-step solution
aligned & ^2 10^ + ^2 50^ - 40^ 80^ & = 1 2 [2 ^2 10^ +2 ^2 50^ -2 40^ 80^ ] & = 1 2 [1+ 20^ +1+ 100^ . & .- (40^ -80^ )- (40^ +80^ ) ] & 2 ^2 A=1+ 2 A and 2 A B . & = (A-B)- (A+B) & = 1 2 [2+ 20^ + 100^ - 40^ + 120^ ] & 1 2 [2+ 20^ + 100^ - 40^ + (- 1 2 ) ] & [ (- )= , (120^ )=- 1 2 ] & aligned aligned & = 1 2 [2- 1 2 +2 ( 20+100 2 )^ ( 80 2 )^ - 40^ ] & = 1 2 [ 3 2 +2 60^ 40^ - 40^ ] & = 1 2 [ 3 2 +2 1 2 40^ - 40^ ] & = 1 2 [ 3 2 + 40^ - 40^ ]= 1 2 3 2 = 3 4 aligned