यदि $\tan x = \frac{2b}{a - c}$ $(a \ne c)$,$y = a \cos^2 x + 2b \sin x \cos x + c \sin^2 x$ और $z = a \sin^2 x - 2b \sin x \cos x + c \cos^2 x$ है,तो:

  • A
    $y = z$
  • B
    $y + z = a + c$
  • C
    $y - z = a + c$
  • D
    $y - z = (a - c)^2 + 4b^2$

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यदि $\tan \left(\frac{\pi}{4}+\frac{y}{2}\right)=\tan ^3\left(\frac{\pi}{4}+\frac{x}{2}\right)$ है,तो $\frac{3 \sin x+\sin ^3 x}{1+3 \sin ^2 x}=$

किसी भी $\theta \in \left( \frac{\pi}{4}, \frac{\pi}{2} \right)$ के लिए,व्यंजक $3(\sin \theta - \cos \theta)^4 + 6(\sin \theta + \cos \theta)^2 + 4\sin^6 \theta$ का मान है

$6(\sin^6 \theta + \cos^6 \theta) - 9(\sin^4 \theta + \cos^4 \theta) + 4$ का मान है

समीकरण $\cos x - x + \frac{1}{2} = 0$ का एक मूल किस अंतराल में स्थित है?

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$\sin ^2 5^{\circ}+\sin ^2 10^{\circ}+\sin ^2 15^{\circ}+\ldots+\sin ^2 90^{\circ}$ का मान ज्ञात कीजिए।

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