Advertisements
Advertisements
Question
(1 + sin A)(1 – sin A) is equal to ______.
Options
cosec2A
sin2A
sec2A
cos2A
Solution
(1 + sin A)(1 – sin A) is equal to cos2A.
Explanation:
(1 + sin A)(1 – sin A) = (1)2 – (sin A)2 ......{(a + b)(a – b) = (a2 – b2)}
= 1 – sin2A
= cos2A
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
Prove the following trigonometric identities.
`(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A`
Prove the following trigonometric identities.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
Prove the following identities:
`((1 + tan^2A)cotA)/(cosec^2A) = tan A`
If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m2 – n2 = a2 – b2
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to
If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ
Prove that
sec2A – cosec2A = `(2sin^2"A" - 1)/(sin^2"A"*cos^2"A")`