Advertisements
Advertisements
प्रश्न
What is the value of \[\frac{\tan^2 \theta - \sec^2 \theta}{\cot^2 \theta - {cosec}^2 \theta}\]
उत्तर
We have,
\[\frac{\tan^2 \theta - \sec^2 \theta}{\cot^2 \theta - {cosec}^2 \theta}\]=` (-1(sec ^2 θ-tan ^2θ ))/(-1 (cosec^2 θ-cot ^2 θ))`
=`( secx^2θ-tan^2 θ)/ (cosec ^2 θ-cot^2 θ)`
We know that,
`sec^2θ-tan ^2θ=1`
` cosec^2 θ-cot ^2θ=1`
Therefore,
`(tan ^2θ-sec^2 θ)/(cot^2θ-cosec^2 θ)=1/1`
=1
APPEARS IN
संबंधित प्रश्न
Prove that (1 + cot θ – cosec θ)(1+ tan θ + sec θ) = 2
Prove the following trigonometric identities.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
Prove the following identities:
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove that:
2 sin2 A + cos4 A = 1 + sin4 A
Show that : `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec A cosec A`
Prove that:
(tan A + cot A) (cosec A – sin A) (sec A – cos A) = 1
If `( sin theta + cos theta ) = sqrt(2) , " prove that " cot theta = ( sqrt(2)+1)`.
Write the value of sin A cos (90° − A) + cos A sin (90° − A).
If 5x = sec θ and \[\frac{5}{x} = \tan \theta\]find the value of \[5\left( x^2 - \frac{1}{x^2} \right)\]
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
Prove the following identity :
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove the following identity :
`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
Choose the correct alternative:
tan (90 – θ) = ?
If tan θ × A = sin θ, then A = ?
If 2 cos θ + sin θ = `1(θ ≠ π/2)`, then 7 cos θ + 6 sin θ is equal to ______.
