Question

write all the other trigonometric ratios of angle a in terms of cosec a​

Answer 1

Answer:

This is for sec A

We know,

cosA= 1/sec A

We know,

sin²A+cos²A=1

sin²A=1−cos²A

sinA= √1-(1/sec A)²

= √ sec² A - 1 / sec² A

∴sinA = √ sec² A - 1 / sec² A

We know,

cosec A= 1/sin A

∴cosec A= sec A / √ sec² A - 1

We know,

cotA= cosA / sinA = sinA / cosA

= 1/sec A/ √ sec² A - 1 / secA

cotA = 1/ √ sec² A - 1

We know ,

tan A = 1/cot A

∴tanA= √sec ²A−1

This is for cosecA

cosec A = 1 / sin A

cosec A = 1 / √(1 + cos2A) - - - - - - - Replacin sin A as√(1 + cos2A) from the identity sin2A + cos2A = 1

cosec A = √(1 + cot2A) - - - - - - - - -Since we know the identity cosec2 A = 1 + cot2A

cosec A = √(1 + 1 / tan2A) - - - - - - - - -Replacing cot2A as 1 / tan2A

cosec A = √(1 + 1 / sec2A - 1) - - - - - - - - - - Replacing tan2A as sec2A - 1 from the identity tan2A +1 = sec2A

Step-by-step explanation:

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Answer 2

Answer:

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