Advertisements
Advertisements
प्रश्न
Write the value of tan1° tan 2° ........ tan 89° .
उत्तर
Tan 1° tan 2° … tan 89°
= tan 1° tan 2° tan 3° … tan 45° … tan 87° tan 88° tan 89°
= tan 1° tan 2° tan 3° … tan 45° … cot(90° − 87° ) cot(90° − 88° ) cot(90° − 89° )
= tan 1° tan 2° tan 3° … tan 45° … cot 3° cot 2° cot 1°
`= tan 1° × tan 2° × tan 3° × …× 1 × …× 1/( tan 3° )xx 1/ (tan 2°) xx 1/ (tan 1°)`
= 1
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
Prove the following trigonometric identity:
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
Prove the following trigonometric identities.
if x = a cos^3 theta, y = b sin^3 theta` " prove that " `(x/a)^(2/3) + (y/b)^(2/3) = 1`
Prove the following identities:
`tan A - cot A = (1 - 2cos^2A)/(sin A cos A)`
Prove the following identities:
`1/(1 + cosA) + 1/(1 - cosA) = 2cosec^2A`
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove the following identities:
`(1 - 2sin^2A)^2/(cos^4A - sin^4A) = 2cos^2A - 1`
`(1+ cos theta)(1- costheta )(1+cos^2 theta)=1`
`sec theta (1- sin theta )( sec theta + tan theta )=1`
If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.
If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, then\[\frac{x^2}{a^2} + \frac{y^2}{b^2}\]
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
Prove the following identity :
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove that :
2(sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) + 1 = 0
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
Prove that `((tan 20°)/(cosec 70°))^2 + ((cot 20°)/(sec 70°))^2 = 1`
Prove that `(tan θ + sin θ)/(tan θ - sin θ) = (sec θ + 1)/(sec θ - 1)`
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
sin2θ + sin2(90 – θ) = ?
