Exam (elaborations)
Trignometry Assignment
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This is for practice for Trigonometry and clearing the basic concepts.
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Pradeep ClassesCLASS XI
TRIGONOMETRIC FUNCTION
Q.1 If ABCD is a cyclic quadrilateral, then show that:
cosA + cosB + cosC + cosD = 0
Q.2 Prove that: tan500 = tan400 + 2tan100
cos 26 0 + sin 26 0
Q.3 Prove that: tan 710 =
cos 26 0 − sin 26 0
m 1 π
Q.4 If tan α = and tan β = , show that α + β = .
m +1 2m + 1 4
π
Q.5 If x − y = , prove that (1 + tanx)(1 + tany) = 2tanx.
4
Q.6 If tanx = p + 1 and tany = p – 1, show that 2cot(x – y) = p2.
k −1
Q.7 If x + y = z and tanx = ktany, than prove that sin (x − y ) = sin z .
k +1
2π 4π
Q.8 Show that: sin α + sin α + + sin α + =0
3 3
1
Q.9 Prove that: cos 20 0. cos 40 0. cos 80 0 =
8
3
Q.10 Prove that: sin 10 0. sin 50 0.sin 60 0.sin 70 0 =
16
π 2π
Q.11 Prove that: 4 sin α sin α + sin α + = sin 3α
3 3
Q.12 If cos(A + B).sin(C – D) = cos(A – B).sin(C + D), then prove that tanA.tanB.tanC + tanD = 0.
α −β k −1 α +β
Q.13 If sinα = ksinβ, prove that tan = tan .
2 k +1 2
sec 8 x − 1 tan 8 x
Q.14 Prove that: =
sec 4 x − 1 tan 2 x
π π
Q.15 Prove that: tan x tan − x . tan + x = tan 3 x .
3 3
Pradeep Gupta/ Math XI/ 8368569239/ e-mail: pradeepclassesmaths@gmail.com/2023 - 24 Page 1 of 4
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