Simplification Questions

• What is the value of sin (–π/3) + cos(–π/6)?
• If θ is acute angle and tan θ – cot θ = 0, then what is the value of tan26θ + cot100θ ?
• If sin 3θ sec 2θ = 1, then what is the value of [3 tan2(5θ/2) – 1] ?
• If a + b + c = 11 and ab + bc + ca = 17, then what is the value of a3 + b3 + c3 – 3abc ?
• If (x/5) + (5/x) = – 2, then what is the value of x3 ?
• What is the simplified value of [2/(cot A – tan A)]?
• What is the simplified value of (sec4 A – tan2 A) – (tan4 A + sec2 A) ?
• If x + (1/x) = 2, then what is the value of x21 + (1/x1331) ?
• Find x, if 5x-6+5x+6 = 6
• When [x + (1/x)] = 5, then what is the value of [x – (1/x)]?
• If x = (√2 + 1)/(√2 – 1), then what is the value of (x5 + x4 + x2 + x)/x3 ?
• If 27x + 27[x–(1/3)] = 972, then what is the value of x?
• The inradius of a equilateral triangle is 10 cm. What is the circum-radius (in cm) of the same triangle?
• If a = 73, b = 74 and c = 75, then what is the value of a3 + b3 + c3 – 3abc ?
• If x2 + (1/x2) = 31/9 and x > 0, then what is the value of x3 + (1/x3) ?
• If x – (1/x) = 3, then what is the value of (2x4 + 3x3 + 13x2 – 3x + 2) / (3x4 + 3) ?
• What is the simplified value of sec6 A – tan6 A – 3 sec2 A tan2 A ?
• What is the simplified value of (cosec A – sin A)(sec A – cos A)(tan A + cot A)?
• What is the simplified value of (cos4 A – sin4 A) ?
• If ab+c=bc+a=Cb+a then which one of the following statements is correct?