sec^6-tan^6=1+3sec^2*tan^2
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nair8539:
sry but i didnt get how did you got sec -tan ?
i could not follow what you are saying
leave it i got the ans thanks for the help btw
Answered by
2
Sec⁶ - tan⁶ = 1 + 3 sec² tan²
L. H. S.
=> ( Sec² - tan² )³
=> ( Sec² ) ³ - ( tan² )³
=> Using identity,
1 + tan² ¢ = sec² ¢
1 = sec² ¢ - tan² ¢
And
x³ - y³ = ( x - y) ( x² + y² + xy )
=> ( Sec² - tan² ) ( sec⁴ + tan⁴ + sec² tan² )
=> 1 [ ( sec² + tan² )² + sec² tan² ]
=> 1 [ ( Sec²)² + ( tan²)² + 2 sec ² tan² + sec² tan² ]
= 1 [ ( sec²)² + (tan²)² + 2 sec ² tan² - 2 sec² tan² + sec² tan ² ]
=> 1 [ ( sec² - tan²) + 2 sec²tan² + sec² tan² ]
=> [ 1 + 3 sec² tan² ]
=> R. H. S.
L. H. S.
=> ( Sec² - tan² )³
=> ( Sec² ) ³ - ( tan² )³
=> Using identity,
1 + tan² ¢ = sec² ¢
1 = sec² ¢ - tan² ¢
And
x³ - y³ = ( x - y) ( x² + y² + xy )
=> ( Sec² - tan² ) ( sec⁴ + tan⁴ + sec² tan² )
=> 1 [ ( sec² + tan² )² + sec² tan² ]
=> 1 [ ( Sec²)² + ( tan²)² + 2 sec ² tan² + sec² tan² ]
= 1 [ ( sec²)² + (tan²)² + 2 sec ² tan² - 2 sec² tan² + sec² tan ² ]
=> 1 [ ( sec² - tan²) + 2 sec²tan² + sec² tan² ]
=> [ 1 + 3 sec² tan² ]
=> R. H. S.
Yes it should be -
No, it is +
Wait. let me edit.
no i just checked google its
its +3ab
in formula
it was a sign mistake
thanks again
Now, it's fine.
Your question was Correct
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