Question

1) If a² + b² + 2ab cos θ = 1 ; c² + d² + 2cd cos θ = 1 and ac + bd + (ad + bc)cos θ = 0 ; then prove that a² + c² = cosec² θ.

2) If x = (sin³ p/cos² p) ; y = (cos³ p/sin² p) and sin p + cos p = 1/2 ; then find the value of x + y.

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Answer 1

Answer:

Question No 1.

$\leadsto$ $\sf If {a}^{2} + {b}^{2} + 2ab cos{\theta} =\: 1; {c}^{2} + {d}^{2} + 2cd cos{\theta} =\: 1 and\: ac + bd + (ad + bc)cos{\theta} =\: 0; then\: prove\: that\: {a}^{2} + {c}^{2} =\: {cosec}^{2}{\theta}$

Question No 2.

$\leadsto$ $\sf If x =\: \bigg(\dfrac{{sin}^{3}p}{{cos}^{2} p}\bigg) ; y =\: \bigg(\dfrac{cos^3p}{sin^2p}\bigg) and\: sin p + cos p =\: \dfrac{1}{2} ; then\: find\: the\: value\: of x + y.$

Solution :-

For the answer please see the refer attachment.

Answer 2

Answer:

your answer is in the attachment