Advertisements
Advertisements
प्रश्न
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
उत्तर
LHS = `(cosecθ)/(tanθ + cotθ)`
= `(1/sinθ)/(sinθ/cosθ + cosθ/sinθ)`
= `(1/sinθ)/((sin^2θ + cos^2θ)/(cosθsinθ))` = `(1/sinθ)/(1/(cosθsinθ)`
= `1/sinθ xx (cosθsinθ)/1 = cosθ`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
sec A (1 − sin A) (sec A + tan A) = 1
Prove that:
`sqrt(sec^2A + cosec^2A) = tanA + cotA`
If `sec theta + tan theta = x," find the value of " sec theta`
Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`tan35^circ cot(90^circ - θ) = 1`
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
sin2θ + sin2(90 – θ) = ?
If cosec A – sin A = p and sec A – cos A = q, then prove that `("p"^2"q")^(2/3) + ("pq"^2)^(2/3)` = 1
If a sinθ + b cosθ = c, then prove that a cosθ – b sinθ = `sqrt(a^2 + b^2 - c^2)`.
