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Express the trigonometric ratios sin A, sec A, tanA in terms of cot A?
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Express the trigonometric ratios sin A, sec A, tanA in terms of cot A?
We know that tanA = 1/cotAso, 1+tan²A = sec²A1+(1/cotA)² = sec²A1+1/cotA = sec²Acot²A+1/cot²A = sec²A√cot²A+1/cot²A = sec√1+cot²A/cotA = secAagain, √1+cot²A/cotA = 1/cosAcosA = cotA/√cot²A+1therefore, sin²A+cos²A = 1sin²A+(cotA/√cot²A+1)² = 1sin²A+cot²A/cot²A+1=1sin²theta = 1= cot²A/cot²A+1sin²A=cot²A+1-cot²A/cot²A+1(cot²A and -cot²A will be cancelled) sin²A= 1/cot²A+1sin²A=√1/cot²A+1= 1/√cot²A+1
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Express the trigonometric ratios sin A, sec A, tanA in terms of cot A?
Trigonometric Ratios in terms of cotangent
Sin A in terms of cot A:
- Sin A = 1/csc A
- Since csc A = 1/sin A
- Sin A = 1/(1/sin A)
- Sin A = sin A
Sec A in terms of cot A:
- Sec A = 1/cos A
- Since cos A = 1/sin A
- Sec A = 1/(1/sin A)
- Sec A = sin A
Tan A in terms of cot A:
- Tan A = sin A/cos A
- Since cos A = 1/sin A
- Tan A = sin A/(1/sin A)
- Tan A = sin^2 A
Explanation:
- By substituting the reciprocal identities, sin A, sec A, and tan A can be expressed in terms of cot A.
- Sin A = sin A, Sec A = sin A, Tan A = sin^2 A.
- These expressions provide alternative ways to represent trigonometric ratios in terms of cotangent.
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Express the trigonometric ratios sin A, sec A, tanA in terms of cot A?
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