Advertisements
Advertisements
प्रश्न
(sec A + tan A) (1 − sin A) = ______.
पर्याय
sec A
sin A
cosec A
cos A
Advertisements
उत्तर
(sec A + tan A) (1 − sin A) = cos A.
Explanation:
The given expression is `(sec "A"+tan "A") (1-sin "A")`.
Simplifying the given expression, we have
`(sec "A"+tan "A")(1-sin "A")`
= `(1/cos "A"+sin "A"/cos "A")(1-sin "A")`
= `(1+sin "A")/(cos"A")xx(1-sin "A")`
= `((1+sin "A")(1-sin "A"))/(cos "A")`
= `(1-sin^2 "A")/cos "A"`
= `cos^2 "A"/cos "A"`
= `cos "A"`
संबंधित प्रश्न
Prove the following trigonometric identities.
`[tan θ + 1/cos θ]^2 + [tan θ - 1/cos θ]^2 = 2((1 + sin^2 θ)/(1 - sin^2 θ))`
Prove the following trigonometric identities.
`(tan A + tan B)/(cot A + cot B) = tan A tan B`
Prove the following identities:
`(1+ sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A) = 2(1 + cot A)`
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`
What is the value of (1 + cot2 θ) sin2 θ?
\[\frac{\sin \theta}{1 + \cos \theta}\]is equal to
\[\frac{1 - \sin \theta}{\cos \theta}\] is equal to
Prove the following identity :
`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
Prove that `(sin θ. cos (90° - θ) cos θ)/sin( 90° - θ) + (cos θ sin (90° - θ) sin θ)/(cos(90° - θ)) = 1`.
Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos2θ
Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`
Choose the correct alternative:
1 + cot2θ = ?
If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ
Prove that
`(cot "A" + "cosec A" - 1)/(cot"A" - "cosec A" + 1) = (1 + cos "A")/"sin A"`
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
sin(45° + θ) – cos(45° – θ) is equal to ______.
(1 – cos2 A) is equal to ______.
