Advertisements
Advertisements
Question
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
Advertisements
Solution
`3 cot^2 theta - 3 cosec ^2 theta`
= `3 ( cot^2 theta - cosec ^2 theta )`
= 3(-1)
=-3
APPEARS IN
RELATED QUESTIONS
If (secA + tanA)(secB + tanB)(secC + tanC) = (secA – tanA)(secB – tanB)(secC – tanC) prove that each of the side is equal to ±1. We have,
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
`Prove the following trigonometric identities.
`(sec A - tan A)^2 = (1 - sin A)/(1 + sin A)`
Prove the following trigonometric identities.
`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`
Prove that
`sqrt((1 + sin θ)/(1 - sin θ)) + sqrt((1 - sin θ)/(1 + sin θ)) = 2 sec θ`
Prove that:
cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A
cosec4 θ − cosec2 θ = cot4 θ + cot2 θ
If `( sin theta + cos theta ) = sqrt(2) , " prove that " cot theta = ( sqrt(2)+1)`.
Find the value of `(cos 38° cosec 52°)/(tan 18° tan 35° tan 60° tan 72° tan 55°)`
From the figure find the value of sinθ.
Define an identity.
If sin θ − cos θ = 0 then the value of sin4θ + cos4θ
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
Without using trigonometric table , evaluate :
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
For ΔABC , prove that :
`sin((A + B)/2) = cos"C/2`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
Find the value of sin 30° + cos 60°.
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 tan2Φ + cot2Φ + 2 = sec2Φ.cosec2Φ.
Prove that `(sin θ + "cosec" θ)/(sin θ) = 2 + cot^2θ`.
