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cosec-2-68-sec-2-56-cot-2-34-tan-2-22-




Question Number 135065 by liberty last updated on 10/Mar/21
cosec^2 68° +sec^2 56° −cot^2 34° −tan^2 22° =?
$$\mathrm{cosec}\:^{\mathrm{2}} \mathrm{68}°\:+\mathrm{sec}\:^{\mathrm{2}} \mathrm{56}°\:−\mathrm{cot}\:^{\mathrm{2}} \mathrm{34}°\:−\mathrm{tan}\:^{\mathrm{2}} \mathrm{22}°\:=? \\ $$
Commented by som(math1967) last updated on 10/Mar/21
2
$$\mathrm{2} \\ $$
Commented by som(math1967) last updated on 10/Mar/21
cosec^2 68−cot^2 (90−22)  +sec^2 56−tan^2 (90−34)  cosec^2 68−cot^2 68+sec^2 56−tan^2 56  =1+1=2
$${cosec}^{\mathrm{2}} \mathrm{68}−{cot}^{\mathrm{2}} \left(\mathrm{90}−\mathrm{22}\right) \\ $$$$+{sec}^{\mathrm{2}} \mathrm{56}−{tan}^{\mathrm{2}} \left(\mathrm{90}−\mathrm{34}\right) \\ $$$${cosec}^{\mathrm{2}} \mathrm{68}−{cot}^{\mathrm{2}} \mathrm{68}+{sec}^{\mathrm{2}} \mathrm{56}−{tan}^{\mathrm{2}} \mathrm{56} \\ $$$$=\mathrm{1}+\mathrm{1}=\mathrm{2} \\ $$

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