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Question
Find A if tan 2A = cot (A-24°).
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Solution
Given :
tan 2A = cot (A-24°)
implies that tan 2A = tan [90° - (A -24°)]
implies that tan 2A = tan [90° - A + 24°]
implies that tan 2A = tan [114° - A ]
implies that 2A = 114° - A
implies that 3A = 114°
implies that A = `(114°)/3`
implies that A = 38°
RELATED QUESTIONS
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(1 + cot2 A) sin2 A = 1
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(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)
Show that one of the values of each member of this equality is sin α sin β sin γ
If `( sin theta + cos theta ) = sqrt(2) , " prove that " cot theta = ( sqrt(2)+1)`.
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If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
`(square + square)/square` = cosec2θ
`square/square` = cosec2θ ......[Taking root on the both side]
cosec θ = `41/9`
and sin θ = `1/("cosec" θ)`
sin θ = `1/square`
∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
Prove the following trigonometry identity:
(sin θ + cos θ)(cosec θ – sec θ) = cosec θ ⋅ sec θ – 2 tan θ
