Advertisements
Advertisements
Question
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
Advertisements
Solution
(sin A + cos A ) sec A
= `( sinA + cos A ) 1/ cos A`
=`(sinA )/( cos A) + ( cos A)/( cos A)`
= tan A + 1
= `5/12 +1/1`
=` (5+12)/12`
=`17/12`
APPEARS IN
RELATED QUESTIONS
If acosθ – bsinθ = c, prove that asinθ + bcosθ = `\pm \sqrt{a^{2}+b^{2}-c^{2}`
Prove the following trigonometric identities.
`sin^2 A + 1/(1 + tan^2 A) = 1`
if `a cos^3 theta + 3a cos theta sin^2 theta = m, a sin^3 theta + 3 a cos^2 theta sin theta = n`Prove that `(m + n)^(2/3) + (m - n)^(2/3)`
`(tan^2theta)/((1+ tan^2 theta))+ cot^2 theta/((1+ cot^2 theta))=1`
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
If `sin theta = x , " write the value of cot "theta .`
If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot2 θ + 2.
If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, then\[\frac{x^2}{a^2} + \frac{y^2}{b^2}\]
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
Without using trigonometric table , evaluate :
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
Prove that:
tan (55° + x) = cot (35° – x)
Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
If cosθ + sinθ = `sqrt2` cosθ, show that cosθ - sinθ = `sqrt2` sinθ.
Prove the following identities:
`(1 - tan^2 θ)/(cot^2 θ - 1) = tan^2 θ`.
sin4A – cos4A = 1 – 2cos2A. For proof of this complete the activity given below.
Activity:
L.H.S = `square`
= (sin2A + cos2A) `(square)`
= `1 (square)` .....`[sin^2"A" + square = 1]`
= `square` – cos2A .....[sin2A = 1 – cos2A]
= `square`
= R.H.S
Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
If 2sin2θ – cos2θ = 2, then find the value of θ.
