If psinA +qcosA=a and pcosA -qsinA =b,then p+a/q+b + q-b/p-a is equal to
Answers
Given :-
- psinA + qcosA = a
- pcosA - qsinA = b
To Find :-
- (p + a)/(q + b) + (q - b)/(p - a) = ?
Solution :-
Let,
→ psinA + qcosA = a -------- Eqn.(1)
→ pcosA - qsinA = b --------- Eqn.(2)
squaring both sides of Eqn.(1) and Eqn.(2) and adding them , we get,
→ (psinA + qcosA)² + (pcosA - qsinA)² = a² + b²
→ [p²sin²A + q²cos²A + 2pq*sinA*cosA] + [p²cos²A + q²sin²A - 2pq*sinA*cosA] = a² + b²
→ (p²sin²A + p²cos²A) + (q²sin²A + q²cos²A) + 2pq*sinA*cosA - 2pq*sinA*cosA = a² + b²
→ p²(sin²A + cos²A) + q²(sin²A + cos²A) = a² + b²
→ p² * 1 + q² * 1 = a² + b²
→ p² + q² = a² + b²
→ p² + q² - a² - b² = 0
→ (p² - a²) + (q² - b²) = 0
→ {(p - a)(p + a)} + {(q - b)(q + b)} = 0
→ (p + a)/(q + b) + (q - b)/(p - a) = 0 (Ans.)
Learn more :-
Learn more :-
It sino + tano = m
tano - sino an
Then express the
values of m²-n² in terms
of M and N
https://brainly.in/question/13926306
tanA/(1-cotA) + cotA/(1-tanA)
https://brainly.in/question/16775946