Advertisements
Advertisements
Question
If `cos theta = 7/25 , "write the value of" ( tan theta + cot theta).`
Advertisements
Solution
`As sin^2 theta = 1 - cos^2 theta`
=` 1- (7/25)^2`
=`1-49/625`
=`(625-49)/625`
⇒ `sin^2 theta = 576/625`
⇒` sintheta = sqrt(576/625)`
⇒`sin theta = 24/25`
Now ,
`tan theta + cot theta `
=`sin theta / cos theta+ cos theta /sin theta`
=`(sin^2 theta + cos^2 theta)/(cos theta sin theta)`
=`1/((7/25xx24/25))`
=`1/((168/625))`
=`625/168`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
Prove that:
cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A
`cosec theta (1+costheta)(cosectheta - cot theta )=1`
If sin θ = `11/61`, find the values of cos θ using trigonometric identity.
If x = a sec θ and y = b tan θ, then b2x2 − a2y2 =
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
Prove the following identity :
`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`
Prove the following identity :
`(cos^3θ + sin^3θ)/(cosθ + sinθ) + (cos^3θ - sin^3θ)/(cosθ - sinθ) = 2`
Evaluate:
`(tan 65°)/(cot 25°)`
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
Prove that `(cot "A" + "cosec A" - 1)/(cot "A" - "cosec A" + 1) = (1 + cos "A")/sin "A"`
Prove the following identities:
`(1 - tan^2 θ)/(cot^2 θ - 1) = tan^2 θ`.
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
If 3 sin θ = 4 cos θ, then sec θ = ?
Prove that `(sintheta + tantheta)/cos theta` = tan θ(1 + sec θ)
Prove that cot2θ – tan2θ = cosec2θ – sec2θ
Prove that `"cot A"/(1 - cot"A") + "tan A"/(1 - tan "A")` = – 1
If cosec A – sin A = p and sec A – cos A = q, then prove that `("p"^2"q")^(2/3) + ("pq"^2)^(2/3)` = 1
If sinθ – cosθ = 0, then the value of (sin4θ + cos4θ) is ______.
