Advertisements
Advertisements
Question
If tan θ = `7/24`, then to find value of cos θ complete the activity given below.
Activity:
sec2θ = 1 + `square` ......[Fundamental tri. identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square/576`
sec2θ = `square/576`
sec θ = `square`
cos θ = `square` .......`[cos theta = 1/sectheta]`
Solution
sec2θ = 1 + tan2θ ......[Fundamental tri. identity]
∴ sec2θ = 1 + `(7/24)^2`
∴ sec2θ = 1 + `49/576`
∴ sec2θ =`(576 + 49)/576`
∴ sec2θ = `625/576`
∴ sec θ = `25/24`
∴ cos θ = `24/25` .......`[cos theta = 1/sectheta]`
RELATED QUESTIONS
Prove the following trigonometric identities.
`sin theta/(1 - cos theta) = cosec theta + cot theta`
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
Show that none of the following is an identity:
`tan^2 theta + sin theta = cos^2 theta`
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`
If 5x = sec ` theta and 5/x = tan theta , " find the value of 5 "( x^2 - 1/( x^2))`
If sinθ = `11/61`, find the values of cosθ using trigonometric identity.
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =
If a cos θ + b sin θ = 4 and a sin θ − b sin θ = 3, then a2 + b2 =
Prove the following identity :
`(1 - cos^2θ)sec^2θ = tan^2θ`
Prove the following identity :
`(secA - 1)/(secA + 1) = sin^2A/(1 + cosA)^2`
Prove that `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`
Without using trigonometric identity , show that :
`sin(50^circ + θ) - cos(40^circ - θ) = 0`
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Prove that :
2(sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) + 1 = 0
Prove the following identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
If cot θ + tan θ = x and sec θ – cos θ = y, then prove that `(x^2y)^(2/3) – (xy^2)^(2/3)` = 1
If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `± sqrt("a"^2 + "b"^2 -"c"^2)`
