Advertisements
Advertisements
प्रश्न
Evaluate sin25° cos65° + cos25° sin65°
उत्तर
sin25° cos65° + cos25° sin65°
=(sin 25°) {cos(90°-25°)}+cos 25°{sin(90°-25)}
=(sin 25°)(sin 25°) + (cos 25°)(cos 25°)
= sin225° + cos225°
= 1 (As sin2A + cos2A = 1)
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`
`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`
`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`
Prove the following trigonometric identities.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
Prove the following trigonometric identities.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
If sin A + cos A = m and sec A + cosec A = n, show that : n (m2 – 1) = 2 m
Write the value of `(1 + tan^2 theta ) cos^2 theta`.
If 5x = sec ` theta and 5/x = tan theta , " find the value of 5 "( x^2 - 1/( x^2))`
\[\frac{1 - \sin \theta}{\cos \theta}\] is equal to
If a cot θ + b cosec θ = p and b cot θ − a cosec θ = q, then p2 − q2
Prove the following identity :
`(1 + tan^2θ)sinθcosθ = tanθ`
If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that `x^2 + y^2 + z^2 = r^2`
Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
Choose the correct alternative:
sec2θ – tan2θ =?
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
The value of 2sinθ can be `a + 1/a`, where a is a positive number, and a ≠ 1.