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Ex 8.4, 1 - Express sin A, sec A and tan A in terms of cot A - Ex 8.4

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Ex 8.4, 1 Express the trigonometric ratios sin A, sec A and tan A in terms of cot A. tan A We know that tan A = ๐Ÿ/๐’„๐’๐’•โก๐‘จ cosec A We know that 1 + cot2 A = cosec2 A cosec2 A = 1 + cot2 A cosec A = ยฑ โˆš(1+๐‘๐‘œ๐‘ก2 ๐ด) Here, A is acute (i.e. less than 90ยฐ) & cosec A is positive when A is acute So, cosec A = โˆš(1+๐‘๐‘œ๐‘ก2 ๐ด) sin A sin A = ๐Ÿ/(๐’„๐’๐’”๐’†๐’„ ๐‘จ) Putting value of cosec A found above sin A = 1/(โˆš(1 + ๐‘๐‘œ๐‘ก2 ๐ด) ) Sec A We know that 1 + tan2 A = sec2 A sec2 A = 1 + tan2 A sec A = ยฑ โˆš((1+๐‘ก๐‘Ž๐‘›2 ๐ด)) Here, A is acute (i.e. less than 90ยฐ) & sec A is positive when A is acute sec A = โˆš((1+๐‘ก๐‘Ž๐‘›2 ๐ด)) sec A = โˆš((1+1/(๐‘๐‘œ๐‘ก2 ๐ด))) sec A = โˆš(((๐‘๐‘œ๐‘ก2 ๐ด + 1)/(๐‘๐‘œ๐‘ก2 ๐ด)) ) sec A = โˆš(๐‘๐‘œ๐‘ก2 ๐ด + 1)/cotโก๐ด

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