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.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
` tan^2 theta - 1/( cos^2 theta )=-1`
`costheta/((1-tan theta))+sin^2theta/((cos theta-sintheta))=(cos theta+ sin theta)`
Show that none of the following is an identity:
(i) `cos^2theta + cos theta =1`
Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50° cosec 40 °`
If `sec theta + tan theta = x," find the value of " sec theta`
What is the value of \[6 \tan^2 \theta - \frac{6}{\cos^2 \theta}\]
Prove the following identity :
`(1 - cos^2θ)sec^2θ = tan^2θ`
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole.
Prove that : `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`
Prove the following identities.
tan4 θ + tan2 θ = sec4 θ – sec2 θ
If cot θ + tan θ = x and sec θ – cos θ = y, then prove that `(x^2y)^(2/3) – (xy^2)^(2/3)` = 1
Prove that cot2θ × sec2θ = cot2θ + 1.
If cosec A – sin A = p and sec A – cos A = q, then prove that `(p^2q)^(2/3) + (pq^2)^(2/3) = 1`.
If 1 + sin2θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
`(cos^2 θ)/(sin^2 θ) - 1/(sin^2 θ)`, in simplified form, is ______.
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
