ANSWER : ± cos α cos β cos γ

Explanation : : (1+sin α) (1+sin β)(1+sin γ)=(1-sin α)(1-sin β)(1-sin γ) =>(1+sin α) (1+sin β)(1+sin γ) / (1-sin α)(1-sin β)(1-sin γ)=1 Multiplying Nr and Dr by (1+sin α) (1+sin β)(1+sin γ) we have (1+sin α)²(1+sin β)²(1+sin γ)²/(1-sin²α)(1-sin²β)(1-sin²γ)=1 =[(1+sin α) (1+sin β)(1+sin γ)]² / cos² α cos² β cos² γ =1 =>[(1+sin α) (1+sin β)(1+sin γ)]²=cos² α cos² β cos² γ =>(1+sin α) (1+sin β)(1+sin γ) =√cos² α √cos² β √cos² γ = ± cos α cos β cos γ

ANSWER : a perfect square of an integer

Explanation : : sin 30°=1/2 cos 45°=1/√2 cos²45°=1/2 Also 1+2+3+..........n=n(n+1) / 2 Now 152(sin30°+2cos²45°+3sin30°+4cos²45°+.......+17sin30°+18cos²45°) =152(1/2+2.1/2+3.1/2+4.1/2+......+17.1/2+18.1/2) =152/2(1+2+3+.........+17+18) =76 x 18x19 / 2 =76x9x19 =4x19x9x19 =2²x3²x19² =(2x3x19)² =perfect square of an integer

ANSWER : √13

Explanation : : Maximum value of asin Ɵ + b cos Ɵ =√a²+√b² Minimum value=√a²+√b² Maximum value of 2sin Ɵ +3cos Ɵ =√2²+√3²=√4+√9=√13

ANSWER : 70 m

Explanation : : Formula: Length of an arc=2πr Ɵ / 360 Where Ɵ is the central angle Let r be the length of the rope.Then 2 x 22 x r x 72 / 7 x 360 = 88 r=88 x 7 x 360 / 2 x 22 x 72 =70m

ANSWER : 160,240,300

Explanation : : A:B=2:3 B:C=4:5 LCM of 3 and 4 =12 A:B=2:3=8:12 B:C=4:5=12:15 A:B:C=8:12:15 Amount to A= 8 / 8 + 12 + 15 x 700 = 8 / 35 x 700=Rs.160 Amount to B=12 /35 x 700 =Rs.240 Amount to C=15 / 35 x 700=Rs.300