Question

if, p = secA and, q = cosecA, prove that p^2 +q^2 = p^2 q^2​

Answer 1

Answer:

Hey,,,, Here is your answer......

sec²A + cosec²A = 1/cos²A + 1/sin²A = Sin²A + cos²A/ sin²A. cos²A = 1/sin²A. cos²A = cosec²A. sec²A......

so, p²+ q² = p².q²......[proved].......

Answer 2

$\huge{\underline{\underline{\rm{AnsWer:-}}}}$

$\bf{Given}\begin{cases}\sf{p=secA}\\ \ \sf{q=cosecA}\end{cases}$

${\underline{\underline{\bf{To\:Prove:-}}}}$

${ \bf{p {}^{2} + q {}^{2} = p {}^{2} q {}^{2} }}$

${\underline{\underline{\bf{Proof:-}}}}$

putting the values of p and q,

sec²A+cosec²=sec²Acosec²A

taking LHS,

→1/cos²A+1/sin²A

→sin²A+cos²A/cos²Asin²A

$\textsf{using identity cos^{2}A+sin^{2}A=1}$

→ 1/cos²Asin²A

→sec²Acosec²A = RHS

#Hence proved :)