What is the simplified value of (cos 4A - sin 4A)?
cos 2A
Apply difference of squares to \(\cos^4 A-\sin^4 A\):
\[\cos^4 A-\sin^4 A=(\cos^2 A-\sin^2 A)(\cos^2 A+\sin^2 A)\]
Using \(\cos^2 A+\sin^2 A=1\) and the double-angle identity \(\cos 2A=\cos^2 A-\sin^2 A\):
\[=\cos 2A\cdot 1=\cos 2A\]
Therefore the simplified value is cos 2A.
Similar Questions
Which of the following will satisfy a2 = b2 + (ab)2 for the values a and b?
If sec x – cos x = 4, then what will be the value of \({{(1 \ + \ cos^2 x)} \over cos x}\)?
In ΔPQR, ∠Q = 90°. If tan R = \(\frac{1}{3}\) then what is the value of \(\rm \frac{secP(cosR+sinP)}{cosecR(sinR-cosecP)}\) ?
What is the value of 5 sin 260° + 7 sin 245° + 8 cos 245° ?
If sec 2θ + tan 2θ = 5/3, then what is the value of tan2θ?
In ΔABC, right angled at B, if tanA = 1/2, then the value of \(\frac{sin A(cos C + cos A)}{cos C (sin C - sin A)}\) is:
The expression \(\rm \frac{(1-sin\,θ+cos\,θ)^2(1-cos\,θ)sec^3\,θ cosec^2\,θ}{(sec\,θ -tan\,θ)(tan\,θ+cot\,θ)} \) , 0° < θ < 90°, is equal to:
If \(\frac {\sec θ + \tan θ }{\sec θ - \tan θ } = 2 \frac {51}{79}, \) then the value of sin θ is equal to:
If \(\frac{{\sec \theta \; - \;\tan \theta }}{{\sec \theta \; + \;\tan \theta }}\; = \;\frac{3}{5},\) then the value of \(\frac{{cosec\theta \; + \;\cot \theta }}{{cosec\;\theta \; - {\rm{\;cot}}\theta }}\) is:
What is the value of \(\frac{3}{2}\left( {\frac{{\cos 39}}{{\sin 51}}} \right) - \sqrt {({{\sin }^2}39 + {{\sin }^2}51})\) ?
Important Questions from Trigonometric Ratios and Identities
What is the ratio of the greatest to the smallest value of 2 – 2 sin x – sin 2x, 0 ≤ x ≤ (π/2)?
If sinθ = \(\frac{4}{5}\) , Find the value of sin3θ
If x, y are acute angles, where 0 < x + y < 90° and sin(3x - 40°) = cos (3y + 40°), then the value of tan (x + y) is equal to
What is (1 + cot θ - cosec θ)(1 + tan θ + sec θ) equal to?
If cos x = p/q and 0° < x < 90°, then the value of tan x is:
