(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

Evaluate the following: sin35° sin45° sec55° sec45°

Evaluate the following: cot20° cot40° cot45° cot50° cot70°

Evaluate the following: cos39° cos48° cos60° cosec42° cosec51°

Evaluate the following: sin(35° + θ) - cos(55° - θ) - tan(42° + θ) + cot(48° - θ)

Evaluate the following: tan(78° + θ) + cosec(42° + θ) - cot(12° - θ) - sec(48° - θ)

Evaluate the following: `(3sin37°)/(cos53°) - (5"cosec"39°)/(sec51°) + (4tan23° tan37° tan67° tan53°)/(cos17° cos67° "cosec"73° "cosec"23°)`

Evaluate the following: `(sin0° sin35° sin55° sin75°)/(cos22° cos64° cos58° cos90°)`

Evaluate the following: `(2sin25° sin35° sec55° sec65°)/(5tan 29° tan45° tan61°) + (3cos20° cos50° cot70° cot40°)/(5tan20° tan50° sin70° sin40°)`

Evaluate the following: `(3sin^2 40°)/(4cos^2 50°) - ("cosec"^2 28°)/(4sec^2 62°) + (cos10° cos25° cos45° "cosec"80°)/(2sin15° sin25° sin45° sin65° sec75°)`

Evaluate the following: `(5cot5° cot15° cot25° cot35° cot45°)/(7tan45° tan55° tan65° tan75° tan85°) + (2"cosec"12° "cosec"24° cos78° cos66°)/(7sin14° sin23° sec76° sec67°)`

If cos3θ = sin(θ - 34°), find the value of θ if 3θ is an acute angle.

If tan4θ = cot(θ + 20°), find the value of θ if 4θ is an acute angle.

If sec2θ = cosec3θ, find the value of θ if it is known that both 2θ and 3θ are acute angles.

If sin(θ - 15°) = cos(θ - 25°), find the value of θ if (θ-15°) and (θ - 25°) are acute angles.

If A, B and C are interior angles of ΔABC, prove that sin`(("A" + "B")/2) = cos  "C"/(2)`

If P, Q and R are the interior angles of ΔPQR, prove that `cot(("Q" + "R")/2) = tan  "P"/(2)`

If cosθ = sin60° and θ is an acute angle find the value of 1- 2 sin²θ

If secθ= cosec30° and θ is an acute angle, find the value of 4 sin²θ - 2 cos²θ.

Prove the following: tanθ tan(90° - θ) = cotθ cot(90° - θ)

Prove the following: sin58° sec32° + cos58° cosec32° = 2