Advertisements
Advertisements
प्रश्न
If cosA + cos2A = 1, then sin2A + sin4A = 1.
विकल्प
True
False
Advertisements
उत्तर
This statement is True.
Explanation:
∵ cosA + cos2A = 1
⇒ cosA = 1 – cos2A = sin2A ...[∵ sin2A + cos2A = 1]
⇒ cos2A = sin4A
⇒ 1 – sin2A = sin4A ...[∵ cos2A = 1 – sin2A]
⇒ sin2A + sin4A = 1
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`
Prove the following identities:
`1 - cos^2A/(1 + sinA) = sinA`
If sin A + cos A = m and sec A + cosec A = n, show that : n (m2 – 1) = 2 m
`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`
If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`
If m = ` ( cos theta - sin theta ) and n = ( cos theta + sin theta ) "then show that" sqrt(m/n) + sqrt(n/m) = 2/sqrt(1-tan^2 theta)`.
What is the value of \[6 \tan^2 \theta - \frac{6}{\cos^2 \theta}\]
The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Prove the following identity :
`(1 + tan^2θ)sinθcosθ = tanθ`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
Prove that :(sinθ+cosecθ)2+(cosθ+ secθ)2 = 7 + tan2 θ+cot2 θ.
If sin θ = `1/2`, then find the value of θ.
If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2 A)`.
If `cos theta/(1 + sin theta) = 1/"a"`, then prove that `("a"^2 - 1)/("a"^2 + 1)` = sin θ
If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
Show that, cotθ + tanθ = cosecθ × secθ
Solution :
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(square + square)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
