Question

Prove that,
1. SinA.cosecA = 1
2. TanA.cotA = 1
3. CosA.secA = 1

Answer 1

Q.No.1.Solution:-

LHS:

SinA.CosecA

= $\frac{Perpendicular}{Hypotenuse}$×$\frac{Hypotenuse}{Perpendicular}$

= $\frac{BC}{AC}$×$\frac{AC}{BC}$

= 1

Q.No.2.solutuon:-

LHS:

TanA.CotA

= $\frac{Perpendicular}{Base}$×$\frac{Base}{Perpendicular}$

= $\frac{BC}{AB}$× $\frac{AB}{BC}$

= 1

Q.No.3.Solution:-

LHS:

CosASecA

= $\frac{Base}{Hypotenuse}$×$\frac{Hypotenuse}{Base}$

= $\frac{AB}{AC}$×$\frac{AC}{AB}$

= 1