Question
If tan 15° = 2 –√3, what is the value of tan 15º
cot 75°+ tan 75º cot 15°.Solution
tan 15° × cot 75° + tan 75° × cot 15° = tan 15° × tan (90° - 15°) + cot (90° -75°) × cot 15° = tan 15° × tan 15° + cot 15° × cot 15° = (tan15°)2 + (cot 15°)2  Now, given tan 15° = 2 - √3 And cot 15° = 1/tan15° = 1/ (2 - √3) = 2 + √3        [on rationalizing]  Thus, tan 15° × cot 75° + tan 75° × cot 15°  = (tan15°)2 + (cot 15°)2 = (2 - √3)2 + (2 + √3)2 = 7 – 4√3 + 7 + 4√3 = 7 + 7 = 14
‘A’ alone can complete a work in 50 hours. ‘A’ started the work alone and left after working on it for 10 hours. If ‘B’ completed the rest o...
40 tailors can stitch a batch of dresses in 30 days. If 20 tailors started the job and after 15 days ‘u’ more tailors joined them such that the rema...
A can complete a piece of work in 10 days and B can complete it in 15 days. They start working together, but B leaves after 3 days. In how many more day...
- An organization engaged 16 workers to complete a task in 24 days. After 9 days, 6 workers had to leave unexpectedly. How many additional days will it now t...
A contractor planned to complete a project in 5 days by employing ‘a’ workers. But every day exactly 15 workers were absent. As a result, the work g...
Arjun and Sameer can complete a job in 20 days and 25 days respectively. When Arjun, Sameer, and Nikhil work together, they finish it inÂ
M, N and O can complete a task in ‘t’, 100, and ‘t + 20’ days respectively. All three started together, but after 15 days, N dropped out. Then, ...
(x + 7) workers finish 60% of a job in 9 days working 4 hours/day. The remaining work is done by (x + 3) workers in 12 days working 3 hours/day. Find x.
A work can be completed by ‘A’ and ‘B’, alone in 10 days and 12 days, respectively. Find the number of days taken by ‘C’ to complete the sam...
A piece of work consists of 360 identical units. A can do (x + 4) units per day and B can do (x − 2) units per day. They work together for 9 days and ...
Relevant for Exams:
