Advertisements
Advertisements
प्रश्न
Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`
उत्तर
`sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta)`
=`sin^2 theta cos^2 theta sec^2 theta cosec^2 theta `
= ` sin^2 theta xx cos^2 xx 1/cos^2 theta xx1/sin^2 theta`
= 1
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cot^2 A(sec A - 1))/(1 + sin A) = sec^2 A ((1 - sin A)/(1 + sec A))`
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
Prove that
`cot^2A-cot^2B=(cos^2A-cos^2B)/(sin^2Asin^2B)=cosec^2A-cosec^2B`
`cosec theta (1+costheta)(cosectheta - cot theta )=1`
`(1+tan^2theta)(1+cot^2 theta)=1/((sin^2 theta- sin^4theta))`
`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
`(1+ tan theta + cot theta )(sintheta - cos theta) = ((sec theta)/ (cosec^2 theta)-( cosec theta)/(sec^2 theta))`
If 5 `tan theta = 4,"write the value of" ((cos theta - sintheta))/(( cos theta + sin theta))`
If tanθ `= 3/4` then find the value of secθ.
What is the value of 9cot2 θ − 9cosec2 θ?
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.
Prove that: 2(sin6θ + cos6θ) - 3 ( sin4θ + cos4θ) + 1 = 0.
Prove that `(tan θ + sin θ)/(tan θ - sin θ) = (sec θ + 1)/(sec θ - 1)`
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
If `(cos alpha)/(cos beta)` = m and `(cos alpha)/(sin beta)` = n, then prove that (m2 + n2) cos2 β = n2
If (sin α + cosec α)2 + (cos α + sec α)2 = k + tan2α + cot2α, then the value of k is equal to
sin2θ + sin2(90 – θ) = ?
Show that tan 7° × tan 23° × tan 60° × tan 67° × tan 83° = `sqrt(3)`
If `sqrt(3) tan θ` = 1, then find the value of sin2θ – cos2θ.