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Ratio

sin A
sin C sin (90-A)

cos A cos C cos (90-A)

tan A tan C tan (90-A)

cosec A
cosec C cosec (90-A)

sec A sec C sec (90-A)

cot A
cot C cot (90-A)

On comparing the tables, the trigonometric ratios of the complementary angles will be -

sin (90° – A) = cos A,

cos (90° – A) = sin A,

tan (90° – A) = cot A,
cot (90° – A) = tan A,

sec (90° – A) = cosec A,

cosec (90° – A) = sec A
0
Note:Let us check this for A = 0 and 90 0

tan 0° = 0 = cot 90°, sec 0° = 1 = cosec 90° and cosec 0°, tan 90°, cot 0°, sec 90°are
not defined.

Example 1:Without using trigonometric tables, evaluate

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