Difference between revisions of "Pythagorean identity for alternate delta trigonometric functions"
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<strong>[[Pythagorean identity for alternate delta trigonometric functions|Theorem]]:</strong> Let $\mathbb{T}$ be a [[time scale]]. The following formula holds: | <strong>[[Pythagorean identity for alternate delta trigonometric functions|Theorem]]:</strong> Let $\mathbb{T}$ be a [[time scale]]. The following formula holds: | ||
| − | $$\mathrm{c}_{pq}^2(t,s;\mathbb{T})+\mathrm{s}_{pq}(t,s;\mathbb{T})=1,$$ | + | $$\mathrm{c}_{pq}^2(t,s;\mathbb{T})+\mathrm{s}_{pq}^2(t,s;\mathbb{T})=1,$$ |
where $\mathrm{c}_{pq}$ denotes the [[delta cpq|alternative delta cosine]] and $\mathrm{s}_{pq}$ denotes the [[delta spq|alternative delta sine]]. | where $\mathrm{c}_{pq}$ denotes the [[delta cpq|alternative delta cosine]] and $\mathrm{s}_{pq}$ denotes the [[delta spq|alternative delta sine]]. | ||
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Revision as of 22:57, 2 June 2016
Theorem: Let $\mathbb{T}$ be a time scale. The following formula holds: $$\mathrm{c}_{pq}^2(t,s;\mathbb{T})+\mathrm{s}_{pq}^2(t,s;\mathbb{T})=1,$$ where $\mathrm{c}_{pq}$ denotes the alternative delta cosine and $\mathrm{s}_{pq}$ denotes the alternative delta sine.
Proof: █
