48Trigonometry Show that (1 + Cos π/8)(1 + Cos 3π/8)(1 + Cos 5π/8)(1 + Cos 7π/8) = 1/8

Junior Inter Maths 1A Trigonometry VIP Questions with Complete Solutions

TrigonometryBasicFormulas

Show that Tan70 - Tan20 = 2Tan50

Show that Tan72 = Tan18 + 2Tan54

Show that Tan50 - Tan40 = 2Tan10

Show that Tan20 + Tan40 + √3 Tan20Tan40 = √3

Show that Tan 56 - Tan 11 - Tan 56 . Tan 11 = 1

Show That Tan 10 + Tan 35 + Tan 10 . Tan 35 = 1

Show that Tan 100 + Tan 125 + Tan 100 . Tan 125 = 1

If Sin α + Cosec α = 2 then show that Sin^n (α) + Cosec^n (α) = 2

Show That Sin 330 . Cos 120 + Cos 210 . Sin 300 = 1

Show That Cos 100 . Cos 40 + Sin 100 . Sin 40 = 1/2

Show That Cos 340 . Cos 40 + Sin 200 . Sin 140 = 1/2

Show that √3 Cosec 20 - Sec 20 = 4

Show that Cos 35 + Cos 85 + Cos 155 = 0

Show that Cos 42 + Cos 78 + Cos 162 = 0

Show that Cos 55 + Cos 65 + Cos 175 = 0

Find The Period of Sin (5x + 3)

Find The Period of Cos [(4x + 9)/5]

Find The Period of Cos (3x + 5) + 7

Find The Period of Cosec (6 - 5x)

Find the Period of Tan 5x

Find the Minimum & Maximum Value of 5 Sin x + 12 Cos x + 13

Find the Minimum & Maximum Value of 5 Sin x + 12 Cos x - 13

Find the Minimum & Maximum Value of 7 Cos x - 24 Sin x + 5

Find the Minimum & Maximum Value of 13 Cos x + 3√3 Sin x - 4

Find the Minimum & Maximum Value of 3 Cos x + 4 Sin x

Find the Minimum & Maximum Value of Cos(x + π/3) + 2√2 Sin(x + π/3) - 3

Find the Minimum & Maximum Value of 3 Sin x - 4 Cos x

Find the Minimum & Maximum Value of 24Sin x + 7 Cos x

Find the Minimum & Maximum Value of Sin 2x - Cos 2x

If Tan 20 = β then show that Tan 160 - Tan 110 / 1 + Tan 160.Tan 110 = 1 - β^2 / 2β

If Tan 20 = p then show that Tan 610 + Tan 700 / Tan 560 - Tan 470 = 1 - p^2 / 1 + p^2

Show that Cos 9 + Sin 9 / Cos 9 - Sin 9 = Cot 36

If Tan α = Cos 11 + Sin 11 / Cos 11 - Sin 11, α is in third quadrant then find α

If Cos A + Sin A = √2 Cos A thenShowthat Cos A - Sin A = √2 Sin A

If 3 Sin A + 4 Cos A = 5 then Show that 4 Sin A - 3 Cos A = 0

If 3 Sin A + 5 Cos A = 5 then Show that 5 Sin A - 3 Cos A = +/- 3

If A + B = 45 then show that (1+Tan A)(1+Tan B) = 2. Hence deduce that Tan 22 1/2 = √2-1

If A + B = 45 then show that (Cot A-1)(Cot B-1) = 2. Hence deduce that Cot 22 1/2 = √2+1

If A + B = 225 thenshowthat (1 + Cot A)(1 + Cot B) = 2 CotA . CotB

If A - B = 135 then show that (1 - Tan A)(1 + Tan B) = 2

If A + B = 135 then show that (1+Cot A)(1+Cot B) = 2. Hence deduce that Cot 67 1/2 = √2-1

If A + B = 135 then show that (1 - Tan A)(1 - Tan B) = 2. Hence deduce that Tan 67 1/2 = 1 - √2

If A + B + C = 90 then show that Cot A + Cot B + Cot C = Cot A.Cot B.Cot C

If A + B + C = 90 then show that Tan A.Tan B + Tan B.Tan C + Tan C.Tan A = 1

If A + B + C = π then show that Tan A + Tan B + Tan C = Tan A. Tan B. Tan C

If A + B + C = π then show that Cot A . Cot B + Cot B . Cot C+ Cot C . Cot A = 1

Show that Sin^4(π/8) + Sin^4(3π/8) + Sin^4(5π/8) + Sin^4(7π/8) = 3/2

Show that (1 + Cos π/8)(1 + Cos 3π/8)(1 + Cos 5π/8)(1 + Cos 7π/8) = 1/8

Show that (1 + Cos π/10)(1 + Cos 3π/10)(1 + Cos 7π/10)(1 + Cos 9π/10) = 1/16

Show that Cos^4(π/8) + Cos^4(3π/8) + Cos^4(5π/8) + Cos^4(7π/8) = 3/2

Show that Tan β + 2 Tan 2β + 4 Tan 4β + 8 Cot 8β = Cot β

Show that 1/Sin 10 - √3/Cos 10 = 4

Show that 1/Cos 290 + 1/[√3 Sin 250] = 4/√3

Show that Tan(π/20)Tan(3π/20)Tan(5π/20)Tan(7π/20)Tan(9π/20) = 1