If tan A + tan B + tan C = 6, Find cot A cot B cot C If tan A + tan B + tan C = 6, Find cot A cot B cot C Question: If in a triangle \( \triangle ABC \), \[ \tan A+\tan B+\tan C=6 \] then \[ \cot A\cot
If 3 sin x + 4 cos x = 5, Find 4 sin x − 3 cos x If 3 sin x + 4 cos x = 5, Find 4 sin x − 3 cos x Question: If \[ 3\sin x+4\cos x=5 \] then \[ 4\sin x-3\cos x= \] (a) \(0\) (b) \(5\) (c) \(1\)
If 3 sin x + 4 cos x = 5, then 4 sin x – 3 cos x = (a) 0 (b) 5 (c) 1 (d) none of these Read More »
If tan A = a/(a + 1) and tan B = 1/(2a + 1), Find the Value of A + B If tan A = a/(a + 1) and tan B = 1/(2a + 1), Find the Value of A + B Question: If \[ \tan A=\frac{a}{a+1} \] and \[ \tan B=\frac{1}{2a+1} \] then the
Find the Value of tan 20° + tan 40° + √3 tan 20° tan 40° Find the Value of tan 20° + tan 40° + √3 tan 20° tan 40° Question: \[ \tan20^\circ+\tan40^\circ+\sqrt{3}\tan20^\circ\tan40^\circ \] is equal to (a) \(\frac{\sqrt{3}}{4}\) (b) \(\frac{\sqrt{3}}{2}\) (c) \(\sqrt{3}\) (d) \(1\) Solution We use the identity: \[ \tan(A+B) = \frac{\tan A+\tan
tan 20° + tan 40° + √3 tan 20° tan 40° is equal to (a) √3/4 (b) √3/2 (c) √3 (d) 1 Read More »
If A + B + C = π, Find sec A (cos B cos C − sin B sin C) If A + B + C = π, Find sec A (cos B cos C − sin B sin C) Question: If \[ A+B+C=\pi \] then \[ \sec A(\cos B\cos C-\sin B\sin C) \] is
Find the Value of sin²(5π/12) − sin²(π/12) Find the Value of sin²(5π/12) − sin²(π/12) Question: The value of \[ \sin^2\left(\frac{5\pi}{12}\right) – \sin^2\left(\frac{\pi}{12}\right) \] is (a) \(\frac{1}{2}\) (b) \(\frac{\sqrt{3}}{2}\) (c) \(1\) (d) \(0\) Solution We use the identity: \[ \sin^2 A-\sin^2 B = (\sin A-\sin B)(\sin A+\sin B) \] Also, \[ \sin^2 A-\sin^2 B = \sin(A+B)\sin(A-B)
The value of sin²(5π/12) – sin²(π/12) is (a) 1/2 (b) √3/2 (c) 1 (d) 0 Read More »
Prove that (2√3 + 3) sin x + 2√3 cos x Lies Between −(2√3 + √15) and (2√3 + √15) Prove that (2√3 + 3) sin x + 2√3 cos x Lies Between −(2√3 + √15) and (2√3 + √15) Question: Prove that \[ (2\sqrt{3}+3)\sin x+2\sqrt{3}\cos x \] lies between \[ -(2\sqrt{3}+\sqrt{15}) \] and \[
Prove that (2√3 + 3) sin x + 2√3 cos x lies between – (2√3 + √15) and (2√3 + √15). Read More »
Show that sin 100° − sin 10° is Positive Show that sin 100° − sin 10° is Positive Question: Show that \[ \sin100^\circ-\sin10^\circ \] is positive. Solution We use the identity: \[ \sin C-\sin D = 2\cos\left(\frac{C+D}{2}\right) \sin\left(\frac{C-D}{2}\right) \] Taking \[ C=100^\circ, \qquad D=10^\circ \] Then, \[ \sin100^\circ-\sin10^\circ = 2\cos\left(\frac{100^\circ+10^\circ}{2}\right) \sin\left(\frac{100^\circ-10^\circ}{2}\right) \] \[ = 2\cos55^\circ\sin45^\circ
Show that sin 100° – sin 10° is positive. Read More »
Reduce 24 cos x + 7 sin x to the Sine and Cosine of a Single Expression Reduce 24 cos x + 7 sin x to the Sine and Cosine of a Single Expression Question: Reduce the following expression to the sine and cosine of a single expression: \[ 24\cos x+7\sin x \] Solution We
Reduce cos x − sin x to the Sine and Cosine of a Single Expression Reduce cos x − sin x to the Sine and Cosine of a Single Expression Question: Reduce the following expression to the sine and cosine of a single expression: \[ \cos x-\sin x \] Solution We use the standard form: