Question

Express all trigonometric ratios in terms of tan theta

Answer 1

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Answer 2

Answer:

#sin@=tan@/√tan^2@+1

#cos@=1/√1+tan^2@

#tan@=tan@

#cot@=1/tan@

#sec@=√1+tan^2@

#cosec@=√tan^2@+1/tan@

Step by Step Explanation:

Expressing all trigonometry ratio in tan@

Expressing all trigonometry ratio in tan@ 1)sin@=1/cosec@

=1\cosec^2@=1+cot^2@=1/cosec@ √1+cot^2@

#sin@=1/cosec@=1/1+cot^@

=1/√1+cot^@=1/√1+1/tan^2@

=1/√tan^2@+1\tan^2@

=1*√tan^2@/tan^2@+1

=√tan^2@/tan^2@+1 [^2/√]

=tan@\√tan^2@+1

2)cos@=1/sec@=1/sec^2@=1+tan^2@

=sec@=√1+tan^2@

1/sec@ =1/1+tan^2@

cos@=1/√1+tan^2@

3)tan@=tan@

4)cot@=1/tan@

5)sec@=

sec^2@=1+tan^2@

sec@=√1+tan^2@

6)cosec@=1/sin@=1/tan@/√tan^2@+1

=1*√tan^2@+1/tan@

=√tan^2@+1/tan@