Trigonometry MCQs

In ΔABC, right-angled at B, AB = 7 cm and AC - BC = 1 cm. Find the value of sinC.

The expression $$\frac{{{{\tan }^6}\theta - {{\sec }^6}\theta + 3{{\sec }^2}\theta \,{{\tan }^2}\theta }}{{{{\tan }^2}\theta + {{\cot }^2}\theta + 2}}$$     is equal to:

What is the value of 3sin²30° + $$\frac{3}{5}$$cos²60° - 2sec²45°?

The value of cos1° cos2° cos3° ............. cos177° cos178° cos179° is?

If $$x = a{\text{ }}\sec \theta .\cos \phi ,$$     $$y = b{\text{ }}\sec \theta .sin\phi ,$$     $$z = c{\text{ tan}}\theta {\text{.}}$$   then the value of $$\frac{{{x^2}}}{{{a^2}}}$$  + $$\frac{{{y^2}}}{{{b^2}}}$$  - $$\frac{{{z^2}}}{{{c^2}}}$$  is?

If tanθ + cotθ = 2, then the value if tan¹⁰⁰θ + cot¹⁰⁰θ is?

ABCD is a rectangle of which AC is a diagonal. The value of (tan² ∠CAD + 1)sin² ∠BAC is?

The value of $$\frac{{4{{\tan }^2}{{30}^ \circ } + {{\sin }^2}{{30}^ \circ }{{\cos }^2}{{45}^ \circ } + {{\sec }^2}{{48}^ \circ } - {{\cot }^2}{{42}^ \circ }}}{{\cos {{37}^ \circ }\sin {{53}^ \circ } + \sin {{37}^ \circ }\cos {{53}^ \circ } + \tan {{18}^ \circ }\tan {{72}^ \circ }}}\,{\text{is:}}$$

What is the value of {sin(90 - x)cos[π - (x - y)]} + {cos(90 - x)sin[π - (y - x)]}?