If \((\cos 35^\circ + \cos 55^\circ) = p\), then what is \(\sin 35^\circ . \cos 35^\circ\) equal to?
\(\dfrac{p^2 - 1}{2}\)
Since \(\cos 55^\circ = \cos(90^\circ - 35^\circ) = \sin 35^\circ\), we get \(p = \cos 35^\circ + \sin 35^\circ\). Squaring, \(p^2 = \cos^2 35^\circ + \sin^2 35^\circ + 2\sin 35^\circ \cos 35^\circ = 1 + 2\sin 35^\circ \cos 35^\circ\). So \(\sin 35^\circ . \cos 35^\circ = \dfrac{p^2 - 1}{2}\).
Similar Questions
If sinθ = (m 2– n 2)/(m 2+ n 2) and 0 < θ < π/2, then what is the value of cosθ?
- What is \((\sec\theta - \tan\theta) - \frac{1-\sin\theta}{1+\sin\theta}\) equal to?
- If \(\cot\theta = \sqrt{7}\), then what is \(\frac{\text{cosec}^2\theta-\sec^2\theta}{\text{cosec}^2\theta+\sec^2\theta}\) equal to?
- What is \((p\sin\theta + q\cos\theta)\) equal to?
- What is \(p^2q^2 (p^2 + q^2+3)\) equal to?
What is sin 4θ - cos 4θ equal to for any real number θ?
What is cot 1° cot 23° cot 45° cot 67° cot 89° equal to?
Consider the following statements:
1. (sec 2θ - 1) (1 - cosec 2θ) = 1
2. sin θ (1 + cos θ) -1 + (1 + cos θ) (sin θ) -1 = 2 cosec θ
Which of the above is/are correct?If sec x cosec x = 2, then what is the tan nx + cot nx equal to?
- If \(3 \sin \theta + 5 \cos \theta = 5\), then what is the value of \(5 \sin \theta - 3 \cos \theta\)?
Important Questions from Trigonometric Identities
What is \(\rm \frac{1+tan^2\theta}{1+cot^2\theta}-\left(\frac{1-tan\theta}{1-cot\theta}\right)^2\) equal to?
If 3sin θ + 5cos θ = 5, then the value of 5sin θ - 3cos θ is equal to:
If angle C of a triangle ABC is a right angle where a, b and c are the sides opposite to the angles A, B and C respectively then what is tan A + tan B equal to?
If \(\sin \left( {A - B} \right) = \frac{1}{2}\) and \(\cos \left( {A + B} \right) = \frac{1}{2}\) , where A > B > 0° and A + B is an acute angle, then the value of A is:
Find the value of $\cos 10^\circ \times \cos 30^\circ \times \cos 50^\circ \times \cos 70^\circ$
