Simplification Questions

• If x2+ x = 19 , then what is the value of (x + 5)2+ [1/(x + 5)2] ?
• What is the simplified value of sec4θ – sec2θ tan2θ ?
• What is the simplified value of (sin A – cosec A)(sec A – cos A) (tan A + cot A)?
• If (1/cos θ) – (1/cot θ) = 1/P, then what is the value of cos θ?
• What is the simplified value of cosec6A – cot6A – 3 cosec2A cot2A ?
• If tan A = 1/2 and tan B = 1/3, then what is the value of tan (2A + B)?
• If a2+b2+c2=83 and a+b+c=15 then the value of ab+bc+ca is
• If 3+12=x+3y, then the x+y is
• If sin (3x 20°) = cos (3y + 20°), then find the value of (x + y).
• If 1/2 is added to a number and the sum is multipled by 3, the result is 21. Then the number is
• If P=9, Q= 17 then the value of p2-q2-13
• If α and β are roots of the equation 3x2 – 13x + 14 = 0 , then what is the value of (α/β) + (β/α)?
• If a + b + c = 9 and ab + bc + ca = 18, then what is the value of a3 + b3 + c3 – 3abc ?
• If 5x = 30-y = 6z , then what is the value of (xy + yz + zx)/xyz?
• If sec (3x – 20°) = cosec (3y + 20°), then what is the value of tan (x + y)?
• If cot A = n/(n + 1) and cot B = 1/(2n + 1), then what is the value of cot (A + B)?
• If angles of measure (5y + 62°) and (22° + y) are supplementary , then value of y is
• If cosαcosβ=m and cosαsinβ=n, then the value of m2+n2 cos2β is
• If 3P/5 = 7Q/2 = 7R/5, then what is the ratio of p, Q and R respectively?
• What is the value of 1xp-q+1+1xq-p+1 ?