If tan (A + B) = √3 and tan (A – B) = 1/√3 0° < A + B < 90°; A > B, find A and B.

 If tan (A + B) = √3 and tan (A – B) = 1/√3
 0° < A + B < 90°; A > B, find A and B.

 

given tan(A + B) = √3 =tan(60 degrees)

 so  A+B=60 degrees -------------------(1)

and tan (A – B) = 1/√3=tan(30 degrees)

A-B=30 degrees--------------(2)

adding the equations

2A = 90 degrrees

A=90/2 = 45 degrees

substitute in (1)

45 + B= 60

B=60-45

 B=15 degrees

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 questions in old cbse sample question papers for 10th  mathematics

if 49x+51y=499 ,51x+49y=501, find the value of x and y

 solution

A had some chocolates, and he divided them into two lots A and B. He sold the first
lot at the rate of ₹2 for 3 chocolates and the second lot at the rate of ₹1 per chocolate, and got a total of ₹400. If he had sold the first lot at the rate of ₹1 per  chocolate, and the second lot at the rate of ₹4 for 5 chocolates, his total collection  would have been ₹460.
Find the total number of chocolates he had.

solution

 

The length of the minute hand of a clock is 6cm. Find the area swept by it when it moves from 7:05 p.m. to 7:40 p.m. 

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n the given figure, arcs have been drawn of radius 7cm each with vertices A, B, C
and D of quadrilateral ABCD as centres. Find the area of the shaded region consisting of the four sectors at the four vertices

 

solution

If sin(A+B) =1 and cos(A-B)= √3/2, 0°< A+B ≤ 90° and A> B, then find the
measures of angles A and B

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Find an acute angle θ when (cosθ − sin θ)/(cosθ+sin θ) = (1−√3)/(1+√3)

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 If the zeroes of the polynomial (x^2) +px +q are double in value to the zeroes of the polynomial 2(x^2 )-5x -3, then find the values of p and q.

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 If A+B=pi/4 show that [1+tan A][1+tanB]=2  or  [1+cotA][1+cotB]=2cotAcotB

https://keral2008.blogspot.com/2024/05/if-abpi4-show-that-1tan-a1tanb2-or.html

Two coins are tossed simultaneously. What is the probability of getting
(i) At least one head?
(ii) At most one tail?
(iii) A head and a tail?

 solution

 To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool?

 solution

 

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.
(i) If the first circular row has 30 seats, how many seats will be there in the 10th row?
(ii) For 1500 seats in the auditorium, how many rows need to be there?

If 1500 seats are to be arranged in the auditorium, how many seats are still left to
be put after 10th row?
(iii) If there were 17 rows in the auditorium, how many seats will be there in the
middle row

solution

 Due to heavy floods in a state, thousands were rendered homeless. 50 schools
collectively decided to provide place and the canvas for 1500 tents and share the
whole expenditure equally. The lower part of each tent is cylindrical with base
radius 2.8 m and height 3.5 m and the upper part is conical with the same base
radius, but of height 2.1 m. If the canvas used to make the tents costs ₹120 per m^2,find the amount shared by each scho15ol to set up the tents

solution

 

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