Download App

Introduction of Trigonometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry1 Mark
Question
The value of $(\tan1^\circ\tan^\circ...\tan89^\circ)$ is equal to _________.
✓

Answer

The value of $(\tan1^\circ\tan^\circ...\tan89^\circ)$ is equal to 1
$=\tan 1^\circ\tan2^\circ\tan3^\circ...\tan89^\circ$
$=\tan (90^\circ-89^\circ)\tan (90^\circ-88^\circ) \\ \tan (90^\circ-87^\circ)...\tan 87^\circ \tan 88^\circ\tan 89^\circ$
$=\cot 89^\circ\cot 88^\circ \cot 87^\circ...\tan 87^\circ \tan 88^\circ\tan 89^\circ$
$=(\cot 89^\circ\tan 89^\circ) (\cot 88^\circ\tan 88^\circ)\\ (\cot 87^\circ\tan 87^\circ)...(\cot 44^\circ\tan44^\circ)(\tan 45^\circ)$
$=1\times1\times1...\times1 \ \ (\because\cot\theta\tan\theta=1\text{and}\tan45^\circ=1)$
$\therefore\tan1^\circ\tan2^\circ\tan3^\circ...\tan89^\circ=1$

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 "Fill In The Blanks[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

The quadratic polynomials, the sum and product of whose zeroes are 7 and 12 are given by __________.
→
All circles are ________ (congruent, similar).
→
If one root of the quadratic equation $3 x^2-10 x+k=0$ is reciprocal of the other, then k = __________.
→
The distance of the point (–3, 4) from Y – axis is _________.
→
If $A^c$ or $\bar{A}$ or $A^{\prime}$ denote the complement of an event $A$, then $P\left(A^c\right)$ = ____________ .
→
The probability of any event associated to a random experiment cannot exceed ____________ .
→
If the arithmetic mean of the roots of the equation $x(x-2)+4 a x=5$ is 3, then a =__________.
→
The range of probability of any event of a random experiment is ____________ .
→
If $\sin \theta+\cos \theta=1$ and $0^{\circ} \leq \theta \leq 90^{\circ}$, then the possible values of $\theta$ are ____________ .
→
If a and b are two positive co-prime integers such that a = 12b then HCF (a, 12)=__________.
→