If cos4θ - sin4θ = k, then the value of \({1-k}\over{1+k}\) is:
tan2θ
The correct answer is Option 2 i.e. tan2θ.
cos4θ - sin4θ = k
⇒ (cos2θ)2 - (sin2θ)2 = k
⇒ (cos2θ - sin2θ)(cos2θ + sin2θ) = k
⇒ cos2θ - sin2θ = k
⇒ \({1-k}\over{1+k}\) = \({1-(cos^2θ - sin^2θ)}\over{1+(cos^2θ - sin^2θ)}\) [sin2θ + cos2θ = 1]
⇒ \({(1-cos^2θ) +sin^2θ}\over{(1-sin^2θ) + cos^2θ}\)
⇒ \({sin^2θ +sin^2θ}\over{cos^2θ + cos^2θ}\)
⇒ \({2sin^2θ}\over{2cos^2θ }\) = \({sin^2θ}\over{cos^2θ }\) = tan2θ
Similar Questions
Simplify: (1 - sec2θ)(1 - sinθ)(1 + sinθ)(1 + cot2θ)
From a point on the ground, the angles of elevation of the top and the bottom of a flag that is mounted on an 18 m high pole are respectively 60° and 30°. The height of the flag is:
If θ is an acute angle, find the denominator D when,
(cotθ - cosecθ)2 = \((1 - cosθ)\over D\)
Simplify the expression: sinA + \(cosA\over tan(90-A)\)
\(cos45° \over{tan30°+ cot60°}\) is equal to:
If sec4A = cosec(3A - 50°), where 4A and 3A are acute angles, find the value of cosec(A + 25°).
Which of the following options gives the correct expression for y when \({cos^2A}\over{1-sinA}\) = y, and sinA ≠ 1?
If \(\sin \theta = \frac{3}{5}\), find \(\cos \theta\).
- Simplify: \(\frac{\sin A}{1-\cos A} + \frac{1-\cos A}{\sin A}\)
- If \(6\sin y + \cos y = \sqrt{9}\sin y\), find the value of \(\tan y\).
Important Questions from Trigonometry
(secθ + tanθ)/(secθ - tanθ) is equal to:
If tan 45°, cot θ then the value of θ, in radians is
ABC is a triangle If sin (A+B)/2 = √3/2, then the value of sin C/2 is
The angles of elevation of the top of a temple, from the foot and the top of a building 30 m high, are 60° and 30° respectively. Then height of the temple is
what is the principal value of \(\sin^{-1} \left( \sin \dfrac{2 \pi}{3} \right)\) ?
