Question
Write the value of $\tan10^\circ\tan15^\circ\tan75^\circ\tan80^\circ?$
✓
Answer
We have to find: $\tan10^\circ\tan15^\circ\tan75^\circ\tan80^\circ$
$=\tan10^\circ\tan15^\circ\tan75^\circ\tan80^\circ$
$=\tan\big(90^\circ-80^\circ\big)\tan\big(90^\circ-75^\circ\big)\tan75^\circ\tan80^\circ$
$=\cot80^\circ\cot75^\circ\tan75^\circ\tan80^\circ$
$=\big(\cot75^\circ\tan75^\circ\big)\big(\cot80^\circ\tan80^\circ\big)$ $\big[\tan\big(90^\circ-\theta\big)=\cot\theta\big]$
$=1\times1$
$=1$ $\big[\cot\theta.\tan\theta=1\big]$
Hence the value of $\tan10^\circ\tan15^\circ\tan75^\circ\tan80^\circ\text{ is }1$
$=\tan10^\circ\tan15^\circ\tan75^\circ\tan80^\circ$
$=\tan\big(90^\circ-80^\circ\big)\tan\big(90^\circ-75^\circ\big)\tan75^\circ\tan80^\circ$
$=\cot80^\circ\cot75^\circ\tan75^\circ\tan80^\circ$
$=\big(\cot75^\circ\tan75^\circ\big)\big(\cot80^\circ\tan80^\circ\big)$ $\big[\tan\big(90^\circ-\theta\big)=\cot\theta\big]$
$=1\times1$
$=1$ $\big[\cot\theta.\tan\theta=1\big]$
Hence the value of $\tan10^\circ\tan15^\circ\tan75^\circ\tan80^\circ\text{ is }1$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If $3 \sin \theta = 4 \cos \theta,$ then $sec \theta = ?$
→There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn -
shows a number which is a multiple of 5.
shows a number which is a multiple of 5.
As shown in figure 1.57, two poles of height 8 m and 4 m are perpendicular to the ground. If the length of shadow of smaller pole due to sunlight is 6 m then how long will be the shadow of the bigger pole at the same time?
Find the coordinates of midpoint of segment joining $(22, 20)$ and $(0, 16)$
→The volume of a right circular cylinder with its height equal to the radius is$25\frac{1}{7}\text{cm}^3$ Find the height of the cylinder.
→Write the quadratic equations in $a x^2+b x+c=0$ form and find the values of a, b, c.
$x-\frac{6}{x}=5$
→$x-\frac{6}{x}=5$
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is:
Other than an ace.
Other than an ace.
Evaluate:
$\text{cosec }(65^\circ+\theta)-\sec(25^\circ-\theta)-\tan(55^\circ-\theta)+\cot(35^\circ+\theta)$
→$\text{cosec }(65^\circ+\theta)-\sec(25^\circ-\theta)-\tan(55^\circ-\theta)+\cot(35^\circ+\theta)$
Find the discriminant of the following equation:
$2x^2 - 7x + 6 = 0$
→$2x^2 - 7x + 6 = 0$
Which of the following are quadratic equations?
$3x^2 - 5x + 9 = x^2 - 7x + 3$
→$3x^2 - 5x + 9 = x^2 - 7x + 3$