Advertisements
Advertisements
प्रश्न
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
Advertisements
उत्तर
Sin4θ – cos4θ = 1 – 2cos2θ
LHS = Sin4θ – cos4θ
LHS = (Sin2θ)2 – (cos2θ)2
LHS = (Sin2θ + cos2θ)(Sin2θ - cos2θ) ...[a2 – b2 = (a + b)(a – b)]
LHS = (Sin2θ – cos2θ).(1) ...(Sin2θ + cos2θ = 1)
LHS = 1 – cos2θ – cos2θ ...(1 – Sin2θ = cos2θ)
LHS = 1 – 2cos2θ
RHS = 1 – 2cos2θ
LHS = RHS
Hence proved.
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 that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
Prove the following identities:
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove that:
(1 + tan A . tan B)2 + (tan A – tan B)2 = sec2 A sec2 B
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
Prove that:
`sqrt(sec^2A + cosec^2A) = tanA + cotA`
`(1+tan^2theta)(1+cot^2 theta)=1/((sin^2 theta- sin^4theta))`
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
`sqrt((1 + sin θ)/(1 - sin θ)) = sec θ + tan θ`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
Show that none of the following is an identity:
`sin^2 theta + sin theta = 2`
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that (m2 + n2) = (a2 + b2).
If `cot theta = 1/ sqrt(3)`, write the value of `((1 - cos^2 theta))/((2 - sin^2 theta))`.
Prove that:
`"tanθ"/("secθ" – 1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`
Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A
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 tan2Φ + cot2Φ + 2 = sec2Φ.cosec2Φ.
cos θ . sec θ = ?
