Q. if asecx - btanx = 1 and a²sec²x - b²tan²x = 5 , then (4a² - 9b²) = ?
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asec x - btanx = 1 ........ (1)
a^2 sec^2 - b ^2 tan ^2 x = 5 .... (2)
: from 2
(asecx + b tanx ) ( a secx - b tan x ) = 5
using 1 we have
asex + btanx = 5 .......(3)
adding 1 and 3 we have
2a secx = 6
asecx = 3
a = 3/ secx
a = 3 cos x ......4
now subtracting 1 from 5
we have
2b tanx = 4
btanx = 2
b = 2/ tanx
b = 2cot .......6
now put these in the required eq and get the answer .
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a^2 sec^2 - b ^2 tan ^2 x = 5 .... (2)
: from 2
(asecx + b tanx ) ( a secx - b tan x ) = 5
using 1 we have
asex + btanx = 5 .......(3)
adding 1 and 3 we have
2a secx = 6
asecx = 3
a = 3/ secx
a = 3 cos x ......4
now subtracting 1 from 5
we have
2b tanx = 4
btanx = 2
b = 2/ tanx
b = 2cot .......6
now put these in the required eq and get the answer .
mark this ans as a brainliest ans
mark it as a brainliet plz
thank you
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