Question

math question need answer asap
try to answer all 3 plz​

Answer 1

Answer:

hey here are your answers of jee mains

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Step-by-step explanation:

$1. \\ so \: here \: \\ x = \gamma .sin \: θ.cosθ \\ y = \gamma .sinθ.sinθ = \gamma .sin {}^{2} θ \\ z = cos θ \\ so \: squaring \: all \: terms \: we \: get \\ x {}^{2} = \gamma {}^{2} .sin {}^{2} θ.cos {}^{2} θ \\ y = \gamma {}^{2} .sin {}^{4} θ \\ z = \gamma .cos {}^{2} θ \\ adding \: all \: terms \: we \: get \\ x {}^{2} + y {}^{2} + z {}^{2} = (\gamma {}^{2} .sin {}^{2} θ.cos {}^{2} θ) + ( \gamma {}^{2} .sin {}^{4} θ) + ( \gamma {}^{2} .cos {}^{2} θ) \\ = \gamma {}^{2} (sin {}^{2} θ.cos {}^{2} θ + sin {}^{4} θ + cos {}^{2} θ) \\ = \gamma {}^{2} (sin {}^{2} θ(sin {}^{2} θ + cos {}^{2} θ) + cos {}^{2} θ) \\ = \gamma {}^{2} (sin {}^{2} θ(1) + cos {}^{2} θ) \\ = \gamma {}^{2} (sin {}^{2} + cos {}^{2} θ) \\ = \gamma {}^{2} (1) \\ = \gamma {}^{2}$

$3. \\ so \: tan \: 765 \: can \: be \: written \: as \: tan(720 + 45) \: ie \: tan(4\pi + \frac{\pi}{4} ) \\ so \: we \: know \: that \: whenever \: there \: is \: \pi \: in \: any \: trigonometric \: ratio \: there \: is \: no \: change \\ hence \: then \: tan \: 765 = tan \: 45 \\ so \: tan \: 45 = 1 \\ and \: as \: 765 \: lies \: un \: quadrant \: 1 the \: sign \: would \: not \: affect \: it \\ hence \: tan \: 765 \: ie \: tan( \frac{17\pi}{4} ) = 1$

$4. \\ so \: here \: 3 x= sec \: θ \: ie \: x = \frac{sec \:θ }{3} \\ \\ \frac{3}{x} = tan \: θ \: ie \: \frac{1}{x} = \frac{tan \: θ}{3} \\ \\ so \: substituting \: these \: values \: in \: 9(x {}^{2} - \frac{1}{x {}^{2} } ) \\ we \: get \\ 9(x {}^{2} - \frac{1}{ {x}^{2} } ) = 9(( \frac{sec \:θ }{3} ) {}^{2} - ( \frac{tan \: θ}{3} ) {}^{2} ) \\ = 9( \frac{sec {}^{2}θ }{9} - \frac{tan {}^{2}θ }{9} ) \\ = 9( \frac{sec {}^{2}θ - tan {}^{2} θ}{9} ) \\ = sec {}^{2} - tan {}^{2} θ \\ = 1$

$5. \\ so \: here \: \\ ( \frac{11}{cot {}^{2} θ} - \frac{11}{cos {}^{2} θ} ) \\ \\ = 11( \frac{1}{cot {}^{2} θ} - \frac{1}{cos {}^{2}θ } ) \\ \\ = 11(tan {}^{2} θ - sec {}^{2} θ) \\ = 11( - 1) \\ = - 11$