Write ‘True’ or ‘False’ and justify your answer. ( +2)(2 +1)=5 + … - Vidyadip

Question

Write ‘True’ or ‘False’ and justify your answer.
$(\tan\theta+2)(2\tan\theta+1)=5\tan\theta+\sec^2\theta$

✓

Answer

False.LHS$=(\tan\theta+2)(2\tan\theta+1)$
$=\tan\theta(2\tan\theta+1)+2(2\tan\theta+1)$
$=2\tan^2\theta+\tan\theta+4\tan\theta+2$
$=2\tan^2\theta+5\tan\theta+2$
$=2(\tan^2\theta+1)+5\tan\theta$
$=2\sec^2\theta+5\tan\theta\neq$ RHS
Hence, the given statement is false.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "True False[1 Marks ]" from Introduction of Trigonometry→Introduction of Trigonometry — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Write 'True' or 'False' and justify your answer in the following:
The value of $\sin\theta$ is $\text{x}+\frac{1}{\text{x}},$ where 'x' is a positive real number.

State whether the following are true or false. Justify your answer.$\cot \text{A}$ is not defined for $\text{A}=0^\circ.$

Write ‘True’ or ‘False’ and justify your answer.
If $cosA + cos^2A = 1, then sin^2A + sin^4A = 1$

State whether the following statements are true or false. Justify your answer.
A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.

State whether the following are true or false. Justify your answer.$\sin \theta=\frac{4}{3} $ for some angle $\theta.$

Is it true to say that area of a segment of a circle is less than the area of its corresponding sector? Why?

Write ‘True’ or ‘False’ and justify your answer.
If angle between two tangents drawn from a point P to a circle of radius a and centre O is 60°, then $\text{OP}=\text{a}\sqrt{3}.$

Write ‘True’ or ‘False’ and justify your answer.
AB is a diameter of a circle and AC is its chord such that $\angle\text{BAC}=30^\circ.$ If the tangent at C intersects AB extended at D, then BC = BD.

Write whether the following statements are true or false. Justify your answers.
Every quadratic equation has at least one real root.

State whether the following statements are true or false. Justify your answer.
Point P(-4, 2) lies on the line segment joining the points A(-4, 6) and B(-4, -6).