ANSWER : 2

Explanation : : =1+sin²23°/cos²23° - cos²67°/sin²67° + cosec²67°/sec² 23° =1+tan²23° - cot²67° + Sec²(90-67°)/sec² 23° =1+tan²23°-tan²(90° -67°) + Sec² 23°/sec² 23° =1+tan²23°-tan²23°+1=2

ANSWER : 1

Explanation : : x=a cos (90° - Ѳ ) =>x=a Sin Ѳ a/x=1/sin Ѳ =Cosec Ѳ Also y=b cot (90- Ѳ)=b tan Ѳ b/y=1/tan Ѳ=cot Ѳ Now a²/x² - b²/y²=Cosec² Ѳ- Cot² Ѳ=1

ANSWER : 1

Explanation : : Sec Ѳ =Cosec Ф =Sec (90-Ф) Ѳ =90-Ф Ф+0=90° Now Cosec (Ѳ+Ф)=Cosec 90°=1

ANSWER : 0

Explanation : : cos =2x=1=cos 0 2x=0=>x=0

ANSWER : √3:1

Explanation : : A:B=2:1 Let A=2x;B=x Now A+B=90=2x+x=90 3x=90 x=90/3=30° A=2x=2 x 30 =60° B=x =30° Therefore , Sin A : Sin B = Sin 60° :Sin 30° = √3/2 : 1/2 =√3:1