Sec2 54 deg-cot2 36 deg-cosec2 57 deg-tan2 33 deg-2sin2 38 deg-sec2sec2 52 deg-sin245 deg-

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Complementary Trigonometric Ratios

sec2 54 deg...

Question

sec² 54°-cot² 36°/cosec² 57°-tan² 33°+2sin² 38°sec²sec² 52°-sin²45°

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\frac{{sec}^{2} 36 - {cot}^{2} 5}{{csc}^{2} 57 - {tan}^{2} 33} + 2 {sin}^{2} 22 {cos}^{2} 45 {sec}^{2} 68

(i) s e c^{2} θ + c o s e c^{2} θ = s e c^{2} θ c o s e c^{2} θ

(i i) t a n^{2} θ - s i n^{2} θ = t a n^{2} θ s i n^{2} θ

(i i i) t a n^{2} θ + c o t^{2} θ + 2 = s e c^{2} θ c o s e c^{2} θ

\frac{{c o s e c}^{2} 63^{0} + {t a n}^{2} 24^{0}}{{c o t}^{2} 66^{0} + {s e c}^{2} 27^{0}} + \frac{{s i n}^{2} 63^{0} + c o s 63^{0} {s i n 27}^{0} + {s i n 27}^{0} {s e c 63}^{0}}{2 ({c o s e c}^{2} 65^{0} - {t a n}^{2} 25^{0})}

6 {tan}^{2} θ + 54 {cot}^{2} θ + 18

I.

54

A . M . \geq G . M .

6 {tan}^{2} θ, 54 {cot}^{2} θ, 18

II.

54

A . M . \geq G . M .

6 {tan}^{2} θ, 54 {cot}^{2} θ; 18

III.

78

{tan}^{2} θ = {cot}^{2} θ

\frac{{sec}^{2} 54^{o} - {cot}^{2} 36^{o}}{c o {sec}^{2} 57^{o} - {tan}^{2} 33^{o}} + 2 {sin}^{2} 38^{o} {sec}^{2} 52^{o} - {sin}^{2} 45^{o} + \frac{2}{\sqrt{3}} tan 17^{o} tan 60^{o} tan 73^{o}

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