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## Trigonometry Problems ### Polar Coordinates * **(i)** (1, 180°) * **(ii)** (1, 5) * **(iii)** (-1, -1) * **(iv)** (-√3, 1) ### Value of Trigonometric Functions * **(i)** sin 19° * **(ii)** cos 1140° * **(iii)** cot 25° ### Proving Identities * **(i)** (1 + tan2A) + 1 = (1 + 1/tan2A) * **(i...

## Trigonometry Problems ### Polar Coordinates * **(i)** (1, 180°) * **(ii)** (1, 5) * **(iii)** (-1, -1) * **(iv)** (-√3, 1) ### Value of Trigonometric Functions * **(i)** sin 19° * **(ii)** cos 1140° * **(iii)** cot 25° ### Proving Identities * **(i)** (1 + tan2A) + 1 = (1 + 1/tan2A) * **(ii)** (cos A - 1)(cot2A + 1) = -1 * **(iii)** (sinθ + secθ)2 + (cosθ + cosecθ)2 = (1 + cosecθsecθ)2 * **(iv)** (1 + cotθ - cosecθ)(1 + tanθ + secθ) = 1 * **(v)** tan3θ/1 + tan2θ + cot3θ/1 + cot2θ = secθcosecθ - 2sinθcosθ * **(vi)** 1/secθ + tanθ + 1/secθ - tan0 = 1 * **(vii)** sinθ/1 + cosθ + 1 + cosθ/sinθ = 2cosecθ * **(viii)** tanθ/secθ - 1 + secθ/tanθ + 1 = secθ-1/secθ+1 * **(ix)** cosecθ - 1/cosecθ + 1 = cotθ * **(x)** (secA + cosA)(secA - cosA) = tan2A + sin2A * **(xi)** 1 + 3cosec2θcot2θ + cot2θ = cosec2θ * **(xii)** 1 - secθ + tanθ/secθ+tanθ-1 = 1 + seçθ - tanθ/secθ+tanθ+1 ### Elimination of θ * **(1)** *x=3secθ, y = 4tanθ* * **(2)** *x=6cosecθ, y = 8cotθ* * **(3)** *x=4coseθ-5sinθ, y=4sinθ + 5cosθ* * **(4)** *x=5+6cosecθ, y = 3 + 8cotθ* * **(5)** *2x=3-4tanθ, 3y = 5 + 3secθ* ### Finding Permissible Values * **(5)** If 2sin2θ + 3sinθ = 0, Find permissible values of cosθ. * ** (6)** If 2cos2θ - 11cosθ + 5 = 0 find possible values of cosθ. ### Finding Acute Angles * **(7)** Find acute angle θ such that 2cos2θ = 3sin2θ * **(8)** Find the acute angle θ such that 5tan2θ + 3 = 9secθ ### Finding Other Trigonometric Values * **(9)** Find sin θ such that 3cosθ + 4sinθ = 4 * **(10)** If cosecθ + cotθ = 5, then evaluate secθ. ### Finding Values * **(11)** If cotθ = 3/4 and θ < 3π/4 then find the value of 4cosecθ + 5cosθ.