Advertisements
Advertisements
प्रश्न
Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`
Advertisements
उत्तर
LHS = `((sinθ - cosθ + 1)/(sinθ + cosθ - 1)) xx ((sinθ + cosθ + 1)/(sinθ + cosθ + 1))`
LHS = `((sinθ + 1 - cosθ )/(sinθ + cosθ - 1)) xx ((sinθ + 1 + cosθ)/(sinθ + cosθ + 1))`
LHS = `((sinθ + 1)^2 - cos^2θ)/((sinθ + cosθ)^2 - 1^2)`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse of the horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
Prove the following trigonometric identities.
`(1 + sin θ)/cos θ+ cos θ/(1 + sin θ) = 2 sec θ`
Prove that `sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta)) = 2 cosec theta`
Prove the following identities:
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove the following identities:
`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`
Prove the following identities:
`sqrt((1 - sinA)/(1 + sinA)) = cosA/(1 + sinA)`
If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that : x2 + y2 + z2 = r2
If tan A = n tan B and sin A = m sin B , prove that `cos^2 A = ((m^2-1))/((n^2 - 1))`
Write the value of ` sec^2 theta ( 1+ sintheta )(1- sintheta).`
If `cos theta = 7/25 , "write the value of" ( tan theta + cot theta).`
If ` cot A= 4/3 and (A+ B) = 90° ` ,what is the value of tan B?
If `cos B = 3/5 and (A + B) =- 90° ,`find the value of sin A.
If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2?
\[\frac{x^2 - 1}{2x}\] is equal to
\[\frac{1 - \sin \theta}{\cos \theta}\] is equal to
(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to
If cos A + cos2 A = 1, then sin2 A + sin4 A =
(sec A + tan A) (1 − sin A) = ______.
Prove the following identity :
( 1 + cotθ - cosecθ) ( 1 + tanθ + secθ)
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
If sec θ = x + `1/(4"x"), x ≠ 0,` find (sec θ + tan θ)
Prove that sin θ sin( 90° - θ) - cos θ cos( 90° - θ) = 0
Prove that sin2 5° + sin2 10° .......... + sin2 85° + sin2 90° = `9 1/2`.
Prove that sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A.
Prove that `(1 + sec theta - tan theta)/(1 + sec theta + tan theta) = (1 - sin theta)/cos theta`
If tan θ = `x/y`, then cos θ is equal to ______.
